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------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/master30.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD/QEAAAYAJQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABwAAAPwCAAD///8AAAAEAAAALQED AAQAAAAnAf//HAAAAPsC/P8AAAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAEAAAALQEEAAQAAAAuARgABAAAAAIBAQAFAAAACQIAAAACFQAAADIKDwAkAAkAAABT b2x2aW5nIDI9AwACAAEAAgABAAMAAgABAAIABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAEC AiJTeXN0ZW0AAAAAAAAAAAAAGAAAAAIAAACYOhUA5AQAAAQAAAAtAQUABAAAAPABBAAcAAAA+wL9 /wAAAAAAAJABAAAAAABAAABBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAtAQQA BAAAAC4BGAAEAAAAAgEBAAUAAAAJAgAAAAIKAAAAMgoOADUAAgAAAG5kAgACAAQAAAAuAQAABAAA AC0BBQAEAAAA8AEEABwAAAD7Avz/AAAAAAAAkAEAAAAAAEAAAEFyaWFsAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAABAAAAC0BBAAEAAAALgEYAAQAAAACAQEABQAAAAkCAAAAAiUAAAAyCg8AOgAU AAAARGVncmVlIEVxdWF0aW9uczogYXgDAAMAAgACAAIAAwABAAMAAgADAAIAAQACAAIAAgADAAEA AQACAAIABAAAAC4BAAAEAAAALQEFAAQAAADwAQQAHAAAAPsC/f8AAAAAAACQAQAAAAAAQAAAQXJp YWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEEAAQAAAAuARgABAAAAAIBAQAFAAAA CQIAAAACCgAAADIKDgBkAAIAAAAyIAIAAQAEAAAALgEAAAQAAAAtAQUABAAAAPABBAAcAAAA+wL8 /wAAAAAAAJABAAAAAABAAABBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAtAQQA BAAAAC4BGAAEAAAAAgEBAAUAAAAJAgAAAAIZAAAAMgoPAGcADAAAACsgYnggKyBjID0gMAMAAQAC AAMAAQACAAIAAgABAAMAAQACAAQAAAAuAQAABAAAAC0BBQAEAAAA8AEEAAMAAAAAAA== ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0051.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
To solve ax2 + bx + c =3D 0:
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
To solve ax2 + bx + c =3D 0:
1:  Use the square-root method if the= x-term is missing.
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
To solve ax2 + bx + c =3D 0:
1:  Use the square-root method if the= x-term is missing.
2nd: Try fac= toring it into two binomials.
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0011.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
To solve ax2 + bx + c =3D 0:
1:  Use the square-root method if the= x-term is missing.
2nd: Try fac= toring it into two binomials.
3rd:  Use the quadratic formula (QF).
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
        = ;       The Square-Root Method
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0052.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
        = ;       The Square-Root Method
Use t= he square-root method if there is no
x-ter= m. 
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
        = ;       The Square-Root Method
Use t= he square-root method if there is no
x-ter= m.  To solve it:
I.Solve for the x2 and get the form x2 =3D d
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
        = ;       The Square-Root Method
Use t= he square-root method if there is no
x-ter= m.  To solve it:
I.Solve for the x2 and get the form x2 =3D d
II.Then x =3D ±Öd are= the roots.
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0013_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAACZmQIDjI9YADt= ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0009.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
3x2 =3D 7
 
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
3x2 =3D 7
x2 =3D
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
3x2 =3D 7
x2 =3D        = ;           take roots
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0014_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGwBDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUACAAQ ADUAhAAAAAAAAAsFAAAFCAsLDQ0LCwUAAAUICw0IBQAABQgIDQgFCAAFCwUIDQsIBQgFAA0ICAUA BQsFBQECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwWTICACQmCe5kCMQGGg 6MECiDojicIWyzoLtpnQJRMKcTrjj6GcuRpNFs4XJTGrLQMU60hQm4XHtQrRYgHdrzI8jpa357h8 Tq/b73gsbA/L+/+AgWdlJjlNCHtwO2ZZAUEsDkkiZV5YLm1NEBGSURKcSoRFay8nmEYOJ4qgL6an Aa1HAaJRSGcCpmGvI0BqIqgoqgAhADs= ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
3x2 =3D 7
x2 =3D        = ;           take roots
        x =3D 
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0015_image006.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC3VRLUhDURT+zrlP3Z4Dn9MgIvg02DS4IJhMFtHgVizyNnhDwafiBvO1ZZMgKxbB JCbtIktiUQSDYlOGySCIRcF5/zYY6IUD3zn3+7k/DzdXh9CrLgKHkgqdrRAkEKMEOBjRu12yktxC TGQRcbPZ1GiKhuyst81LceDURVqiie4+DKOpyPBUmkQnsqoCSDhSYzkpLObLa7l4OwTukJDTLzYK tSQRk2S8BzngVVZoQKJ5YWaXXCAzO+YDaun9Dj1Z/alkGC47T9Tpzc6L3QswxzbPIjUrCvUu31z9 Mc77pP0ZXm49Ckv+Uljxl7ei/CYejz4qz7J8/7Ny7xVrJof13abdN7HLSpqJTX9LO7qfif/wZ+Wf jaPC1gaw0O9mrhvpf/yFvut7O6fOs1AW57FrX9rVv6GPDZPloUd3F/r/iHk8G5fKYYSa8oVUjGFP CxSh8ZpG6y4mS0Bo/S9+jsxRVAIAAA== ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0015_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNgA/AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABgAt ADUAhAAAAAAAAA0LCwUAAAAABQsLDQ0IBQAFCwsFBQgIDQgFBQ0ICAUFCAsIBQUICwUFCwsFAAUI DQUABQgFCAgFAAAFCAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwX/ICCOZGmeQKCubBug cCy+cm2f9K3b+e6jvZ9wFBz+ikZfTzBwEQpJIMngChyi0hEiQRIouFhTbgEeLRjQcAk5ajjUYpi3 DJ/Bzum6HeXWk9hzfnsneIIpMH2GgF+Gh4QPjY4mEBE1iUdJl0qZb0JsN5o7nzahOqMnDVUrlTxR pa2cnq6dmzOqLKi0orOykTCnqLcBrH9FwFEvKmu+tsvMyn/MKT2ATQFPYdCSJAsSUEzYyDlFAhN5 CwPERtrA6OpD7DUQV1jxcgP02TSAFCv54oNQUAmga92+GujCJYF2DIJCg9tiNKiQZ6G2GAIoFDSI JGGaeXBWnMjI4p24Y3pEAwoJAQA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0015_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGwBDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUACAAQ ADUAhAAAAAAAAAsFAAAFCAsLDQ0LCwUAAAUICw0IBQAABQgIDQgFCAAFCwUIDQsIBQgFAA0ICAUA BQsFBQECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwWTICACQmCe5kCMQGGg 6MECiDojicIWyzoLtpnQJRMKcTrjj6GcuRpNFs4XJTGrLQMU60hQm4XHtQrRYgHdrzI8jpa357h8 Tq/b73gsbA/L+/+AgWdlJjlNCHtwO2ZZAUEsDkkiZV5YLm1NEBGSURKcSoRFay8nmEYOJ4qgL6an Aa1HAaJRSGcCpmGvI0BqIqgoqgAhADs= ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
3x2 =3D 7
x2 =3D        = ;           take roots
        x =3D 
       = 3;
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0016_image009.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC3VSO0gDQRCdnb3E5AyYRAsRi9PCzoAGEaystNIiSS2XwAUFz4gJxHTWqQS7NAYr sbNWJFUQ0WDnp1OChVgIIoiC587u3mFAFxbem5k38272bq7aDZCnGbENFiV0nWEgAF9kAAaMymxI 3Cj6CBnTiKHneRKl2LCO9Qd1MbSNZiQp0ER4AEbAo2KIC94S6FBcOwIQMYRG18RgKV9ZzdU2HeED RBI+USnoiEKYZKr3ENq4goQGBVrgKnaGBaZiB7jHfL3Vo2dafyQqVC0a96y3NxqPOmfDPOp5GlGs yGkvX7jzrTrvMtkfIZ5bc52ytexUrUzJzW/A7f5b9UFcy3qvNhLFjpqD8tumzRY+h2ldM2mf18PU KhXwixDxKc1f+DYST2veYVuSz6b/8IPkJ1tzC6V1gHbCvDvvJv/xw+VuXn/5+jCoxXHg45ITPwn4 HKi8qV/OlK8r1wDKSxz6JDuV/wNDHM/WyhXHhQ7NBaEYg7oUUEH3KQn+bpQXDlzqfwBB6MWQpAIA AA== ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0016_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhfAA/AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABgB1 ADUAhAAAAAAAAA0LCwUAAAAABQsLDQ0IBQAFCwsFBQgIDQgFBQ0ICAUFCAsIBQUICwUFCwsFAAUI DQUABQgFCAAFCAgFAAsICAECAwECAwECAwECAwECAwECAwECAwECAwECAwX/ICCOZGmeQKCubBug cCzPdG3D763vfO+TuZ9wSOwFi8ikcnRcOp+8JnRKRUmrWOxRMHARCtkw8WhwBQ7i9O+ISJAECrd6 rgsu5KMFA0zv064jDQ5+hDKAAHB4hYtAMHp8jJEpMIKSloCJlpGHj5qMh5Wei5hxoqMoCw+mpycQ EX4QAYMyXCsEeLUBXyehO4dVvSRlKrMxDSxoIgsSYFy7JcE3v1TRwrK0eyYCE5ALA6/QxXV91SNl 4q26iife4CTlf+To1vMk3isUkCYQyeFGQ8Py5VlnAh6AczSO6dIngks/hWYCuDM0JBWiCmdEIGAI AKKZiQhpCMDY7+KKkoHq782YRsMCpFwTURgMKXLAM2vX/PnyMzNnjQa32NlkaDDGkYgtUATsRlDn CZo0lnEUAeGmiKI4KqoamRHARhk9VSoVyItsyihDXI6AOSPsjTYoRordKapMyWPFIJB1lWco1WQe XcRMIYWlksAtwN1bMQuvORYTua4YXOOFihKGV2W53EjzqCaZPVPhLAJTl4Wiq5C+IhWR39RQVmvj 1pcy7CKyZbS7/SR3DH68ewf55TB47ByYMKpAaRw3chnD5jaP8lz36+ljqsuoOhU79UkJzXoXskJk BenjbZQ34e0Z8PTZr0hWYRu+L9L2VePPPyMEADs= ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0016_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGwBDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUACAAQ ADUAhAAAAAAAAAsFAAAFCAsLDQ0LCwUAAAUICw0IBQAABQgIDQgFCAAFCwUIDQsIBQgFAA0ICAUA BQsFBQECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwWTICACQmCe5kCMQGGg 6MECiDojicIWyzoLtpnQJRMKcTrjj6GcuRpNFs4XJTGrLQMU60hQm4XHtQrRYgHdrzI8jpa357h8 Tq/b73gsbA/L+/+AgWdlJjlNCHtwO2ZZAUEsDkkiZV5YLm1NEBGSURKcSoRFay8nmEYOJ4qgL6an Aa1HAaJRSGcCpmGvI0BqIqgoqgAhADs= ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0017.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
3x2 =3D 7
x2 =3D        = ;           take roots
        x =3D 
       exa= ct answers
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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The Square-Root Method
Example:   Solve 3x2 – 7 =3D 0 <= /span>
3x2 – 7 =3D 0 solve for x2
3x2 =3D 7
x2 =3D        = ;           take roots
        x =3D 
       exa= ct answers     &nbs= p; approx. answers
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Try factoring the equation into the form
(#x += #)(#x + #) =3D 0.
Solving 2nd Degree Equations: ax<= /span>2 + bx + c =3D 0
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        = ;            Factoring Method
Try factoring the equation into the form
(#x += #)(#x + #) =3D 0.
Hint:=   Find b2 – 4ac, if it is not a perfect
squar= e then the equation is not factorable.
Solving 2nd Degree Equations: ax<= /span>2 + bx + c =3D 0
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        = ;            Factoring Method
Try factoring the equation into the form
(#x += #)(#x + #) =3D 0.
Hint:=   Find b2 – 4ac, if it is not a perfect
sq= uare then the equation is not factorable.
(perf= ect squares: 0, 1, 4, 9, 16, 25,…)
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Examp= le:  Which of the following equations =
is factorable? Solve it by factoring if it is.
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Examp= le:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x= 2 – 2x + 8 =3D 0     b. 3x2 – 2x – 8 =3D 0<= /div>
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Examp= le:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0     b. 3= x2 – 2x – 8 =3D 0
  a =3D 3, b =3D -2, c =3D8
  
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Examp= le:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x= 2 – 2x + 8 =3D 0     b. 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2= , c =3D8
   so b2 = – 4ac
   =3D (-2)2 –= 4(3= )(8)
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Examp= le:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x= 2 – 2x + 8 =3D 0      b. 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8
   so b2 = – 4ac
   =3D (-2)2 = – 4(3)(8)
   =3D 4 –= 96 =3D -92
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8&#= 13;
   so b2 –= 4ac
   =3D (-2)2 –= 4(3)(8)
   =3D 4 –= 96 =3D -92
    Not a perfect square
  &= nbsp; Not factorable
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8        = ;   a =3D 3, b =3D -2, c =3D -8 &= nbsp;
   so b2 –= 4ac
   =3D (-2)2 –= 4(3)(8)
   =3D 4 –= 96 =3D -92
    Not a perfect square
  &= nbsp; Not factorable
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8        = ;   a =3D 3, b =3D -2, c =3D -8 &= nbsp;
   so b2 –= 4ac        = ;            &n= bsp;  b2 = – 4ac =3D (-2)2=  –= 4(3)(-8)  
   =3D (-2)2 –= 4(3)(8)
   =3D 4 –= 96 =3D -92
    Not a perfect square
  &= nbsp; Not factorable
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8        = ;   a =3D 3, b =3D -2, c =3D -8 &= nbsp;
   so b2 –= 4ac        = ;            &n= bsp;  b2 = – 4ac =3D (-2)2=  –= 4(3)(-8)  
   =3D (-2)2 –= 4(3)(8)        = ;        =3D 4 + 96 =3D 100
   =3D 4 –= 96 =3D -92
    Not a perfect square
  &= nbsp; Not factorable
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8        = ;   a =3D 3, b =3D -2, c =3D -8 &= nbsp;
   so b2 –= 4ac        = ;            &n= bsp;  b2 = – 4ac =3D (-2)2=  –= 4(3)(-8)  
   =3D (-2)2 –= 4(3)(8)        = ;        =3D 4 + 96 =3D 100 =3D 102
   =3D 4 –= 96 =3D -92
  &= nbsp; Not a perfect square
  &= nbsp; Not factorable
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8        = ;   a =3D 3, b =3D -2, c =3D -8 &= nbsp;
   so b2 –= 4ac        = ;            &n= bsp;  b2 = – 4ac =3D (-2)2=  –= 4(3)(-8)  
   =3D (-2)2 –= 4(3)(8)        = ;        =3D 4 + 96 =3D 100 =3D 102
   =3D 4 –= 96 =3D -92        = ;          3x2 – 2x – 8 =3D 0<= span lang=3DEN-US style=3D'mso-hansi-font-family:Garamond;font-size:88%;color:#= 33CC33; mso-fareast-language:ZH-CN;display:none'>
    Not a perfect square
  &= nbsp; Not factorable
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8        = ;   a =3D 3, b =3D -2, c =3D -8 &= nbsp;
   so b2 –= 4ac        = ;            &n= bsp;  b2 = – 4ac =3D (-2)2=  –= 4(3)(-8)  
   =3D (-2)2 –= 4(3)(8)        = ;        =3D 4 + 96 =3D 100 =3D 102
   =3D 4 –= 96 =3D -92        = ;          3x2 – 2x – 8 =3D 0<= span lang=3DEN-US style=3D'mso-hansi-font-family:Garamond;font-size:88%;color:#= 33CC33; mso-fareast-language:ZH-CN;display:none'>
    Not a perfect square        = ;            &n= bsp;  (3x + 4)(x – 2) =3D 0
  &= nbsp; Not factorable
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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        = ;            Factoring Method
Example:  Which of the following equations =
is factorable? Solve it by factoring if it is.
a. 3x2 – 2x + 8 =3D 0       b. = 3x2 – 2x – 8 =3D 0
   a =3D 3, b =3D -2, c =3D8        = ;   a =3D 3, b =3D -2, c =3D -8 &= nbsp;
   so b2 –= 4ac        = ;            &n= bsp;  b2 = – 4ac =3D (-2)2=  –= 4(3)(-8)  
   =3D (-2)2 –= 4(3)(8)        = ;        =3D 4 + 96 =3D 100 =3D 102
   =3D 4 –= 96 =3D -92        = ;          3x2 – 2x – 8 =3D 0<= span lang=3DEN-US style=3D'mso-hansi-font-family:Garamond;font-size:88%;color:#= 33CC33; mso-fareast-language:ZH-CN;display:none'>
    Not a perfect square        = ;            &n= bsp;  (3x + 4)(x – 2) =3D 0
  &= nbsp; Not factorable        = ;            &n= bsp;             x =3D -4/3,  x =3D 2
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0030_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhngAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCd ACAAgAAAAAAAAAKLjI+py+0Po5y0JoCz3rz7D4biSJbmiRnoyrbuC3tqTNf2vc74zve17gsKhyAg 8Yj0GZPMJmzpjEpJ0Kn1qqlit1It95v0gsdCMfm8M6PXNDX73XLD5yY5/R6y4/ccPf8P4Ae4Jzh4 V2g4h5j4tsi45vh4Fik5Rln5dYm5pbl51ek5ZTFKWmp6ivpQAAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF):
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0035_image021.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC51SPSwEQRR+83bsub0V5ygQxVKokBASjUSuEvGT3F3U1uWExCFOci5RXBQKFa2G UjSISnKFQnQaDeVJiO5IRENizZuZ3RxRYJNJvu+9773vzdu5ubrcBfkN29McwoR6pxgB44gBcGiT 2RpxwugjZEwjhp7nSdTDmnUsEuhsnObDdkygTrMeWsEjMUQFPxfojJgN0MJFjdbYMO6uzqUKyxmh gVoRfUNVQZ8QQjdTvZtwg13XEGrEWWaYvtb5omVauygUSstx1Pzah2NC5ybh2FQxH1HsIqJiRdxE FSvifYT28o7FD+W2LTfCEaKp+Wwm50xk8k5iKesuwu3eS/5OHMd5zZ82zNYpb5R367NsPhiiSreg eIXFLVqfm/Z5yaT8TMAPjGpexjEgvpb+Pg/8aR5D7uu5aq4V6dsX+K6HifdrH8f7nw9qH0P7xNlO SPn8MD9S32QhO7O0ADCA1lPXQ+yX81fYXC216A7mP+TETwK+j9X5MqbkHxxKW/olWvK1yuuBmi0K IclK8n0zxI5kIbeayUIdzQGioh22ZAEJRh5j8P3Ohqz/BD0pokB0AwAA ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0035_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAB7 ACgAhAAAAAAAAA0LCwUAAAUICwsICAsLDQUABQsFBQgIDQgFAAgFBQ0IBQAFCAUIDQAFCwgIBQsI BQsFAAUFCwAABQ0ICAsIDQsLCwUFBQUFCAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquYuC+ cCzPdF2zeK7rwe7/wKBw1Rsaj8hkESUYBAjJqDS6PBUMgoNhyu36qilEwkvGCRRP5mKLK57TpiuQ 0WCXh2K1nUjKlxgOQE11d0NZeyQCazlLh38PQQgQhIVBDJB6bSSXJREvgTuAEZSVPxIETpQSM5go VaepiD4CEwCje54Uk1tvAaClTRRYA78iirInjQPCTcU/CFu3xgqQTVAVxLZQUasyrZwAZ87HyVVL 4OIq3TGYFWO2qpjizaUmEqBZ7yPkJT3mI/eMHdBnSoYDBsJEVNBCB1khR7Za7VvkaoQbLSIiSBwi 7dQ0SBrrPcqY8EuLEeAiw5Q80rGaEwIWpEmr123jOhgbT75ykZMjIQYuKFxYhgUNHJFI/CFdWg8M 06dQnwKlMAYoqahYg2gMSeLmi55ZwwLAtk2s2VkKnDGywbat27dw48oYEQFDTq88z55lQKBCBgMR COodTDdANTRlCStezLix48eCnPiCTJicJ7WUsbr7mHmxBLCdsaYrrOtqaJF+2Zxxmfi0SD8APk/D 7PpOhF8I2Sx0WNsLX4UJPIaj1rse0BfCZDd5YqF4IU84ARwXShRpCAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=  
b2 – 4ac is called the <= span lang=3DEN-US style=3D'color:#009999;mso-color-index:6;mso-fareast-language= :ZH-CN'>discriminant because its =
value indicates what type of roots th= ere are:
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0036_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAB7 ACgAhAAAAAAAAA0LCwUAAAUICwsICAsLDQUABQsFBQgIDQgFAAgFBQ0IBQAFCAUIDQAFCwgIBQsI BQsFAAUFCwAABQ0ICAsIDQsLCwUFBQUFCAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquYuC+ cCzPdF2zeK7rwe7/wKBw1Rsaj8hkESUYBAjJqDS6PBUMgoNhyu36qilEwkvGCRRP5mKLK57TpiuQ 0WCXh2K1nUjKlxgOQE11d0NZeyQCazlLh38PQQgQhIVBDJB6bSSXJREvgTuAEZSVPxIETpQSM5go VaepiD4CEwCje54Uk1tvAaClTRRYA78iirInjQPCTcU/CFu3xgqQTVAVxLZQUasyrZwAZ87HyVVL 4OIq3TGYFWO2qpjizaUmEqBZ7yPkJT3mI/eMHdBnSoYDBsJEVNBCB1khR7Za7VvkaoQbLSIiSBwi 7dQ0SBrrPcqY8EuLEeAiw5Q80rGaEwIWpEmr123jOhgbT75ykZMjIQYuKFxYhgUNHJFI/CFdWg8M 06dQnwKlMAYoqahYg2gMSeLmi55ZwwLAtk2s2VkKnDGywbat27dw48oYEQFDTq88z55lQKBCBgMR COodTDdANTRlCStezLix48eCnPiCTJicJ7WUsbr7mHmxBLCdsaYrrOtqaJF+2Zxxmfi0SD8APk/D 7PpOhF8I2Sx0WNsLX4UJPIaj1rse0BfCZDd5YqF4IU84ARwXShRpCAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0037.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=  
b2 – 4ac is called the <= span lang=3DEN-US style=3D'color:#009999;mso-color-index:6;mso-fareast-language= :ZH-CN'>discriminant because its =
value indicates what type of roots th= ere are:
•<= /span>If b2 – 4ac is a perf= ect square, we have rational roots.
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0037_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAB7 ACgAhAAAAAAAAA0LCwUAAAUICwsICAsLDQUABQsFBQgIDQgFAAgFBQ0IBQAFCAUIDQAFCwgIBQsI BQsFAAUFCwAABQ0ICAsIDQsLCwUFBQUFCAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquYuC+ cCzPdF2zeK7rwe7/wKBw1Rsaj8hkESUYBAjJqDS6PBUMgoNhyu36qilEwkvGCRRP5mKLK57TpiuQ 0WCXh2K1nUjKlxgOQE11d0NZeyQCazlLh38PQQgQhIVBDJB6bSSXJREvgTuAEZSVPxIETpQSM5go VaepiD4CEwCje54Uk1tvAaClTRRYA78iirInjQPCTcU/CFu3xgqQTVAVxLZQUasyrZwAZ87HyVVL 4OIq3TGYFWO2qpjizaUmEqBZ7yPkJT3mI/eMHdBnSoYDBsJEVNBCB1khR7Za7VvkaoQbLSIiSBwi 7dQ0SBrrPcqY8EuLEeAiw5Q80rGaEwIWpEmr123jOhgbT75ykZMjIQYuKFxYhgUNHJFI/CFdWg8M 06dQnwKlMAYoqahYg2gMSeLmi55ZwwLAtk2s2VkKnDGywbat27dw48oYEQFDTq88z55lQKBCBgMR COodTDdANTRlCStezLix48eCnPiCTJicJ7WUsbr7mHmxBLCdsaYrrOtqaJF+2Zxxmfi0SD8APk/D 7PpOhF8I2Sx0WNsLX4UJPIaj1rse0BfCZDd5YqF4IU84ARwXShRpCAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=  
b2 – 4ac is called the <= span lang=3DEN-US style=3D'color:#009999;mso-color-index:6;mso-fareast-language= :ZH-CN'>discriminant because its =
value indicates what type of roots th= ere are:
•<= /span>If b2 – 4ac is a perf= ect square, we have rational roots.
•If b2 – 4ac < 0 th= ere is no real roots
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0038_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAB7 ACgAhAAAAAAAAA0LCwUAAAUICwsICAsLDQUABQsFBQgIDQgFAAgFBQ0IBQAFCAUIDQAFCwgIBQsI BQsFAAUFCwAABQ0ICAsIDQsLCwUFBQUFCAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquYuC+ cCzPdF2zeK7rwe7/wKBw1Rsaj8hkESUYBAjJqDS6PBUMgoNhyu36qilEwkvGCRRP5mKLK57TpiuQ 0WCXh2K1nUjKlxgOQE11d0NZeyQCazlLh38PQQgQhIVBDJB6bSSXJREvgTuAEZSVPxIETpQSM5go VaepiD4CEwCje54Uk1tvAaClTRRYA78iirInjQPCTcU/CFu3xgqQTVAVxLZQUasyrZwAZ87HyVVL 4OIq3TGYFWO2qpjizaUmEqBZ7yPkJT3mI/eMHdBnSoYDBsJEVNBCB1khR7Za7VvkaoQbLSIiSBwi 7dQ0SBrrPcqY8EuLEeAiw5Q80rGaEwIWpEmr123jOhgbT75ykZMjIQYuKFxYhgUNHJFI/CFdWg8M 06dQnwKlMAYoqahYg2gMSeLmi55ZwwLAtk2s2VkKnDGywbat27dw48oYEQFDTq88z55lQKBCBgMR COodTDdANTRlCStezLix48eCnPiCTJicJ7WUsbr7mHmxBLCdsaYrrOtqaJF+2Zxxmfi0SD8APk/D 7PpOhF8I2Sx0WNsLX4UJPIaj1rse0BfCZDd5YqF4IU84ARwXShRpCAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0039_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAB7 ACgAhAAAAAAAAA0LCwUAAAUICwsICAsLDQUABQsFBQgIDQgFAAgFBQ0IBQAFCAUIDQAFCwgIBQsI BQsFAAUFCwAABQ0ICAsIDQsLCwUFBQUFCAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquYuC+ cCzPdF2zeK7rwe7/wKBw1Rsaj8hkESUYBAjJqDS6PBUMgoNhyu36qilEwkvGCRRP5mKLK57TpiuQ 0WCXh2K1nUjKlxgOQE11d0NZeyQCazlLh38PQQgQhIVBDJB6bSSXJREvgTuAEZSVPxIETpQSM5go VaepiD4CEwCje54Uk1tvAaClTRRYA78iirInjQPCTcU/CFu3xgqQTVAVxLZQUasyrZwAZ87HyVVL 4OIq3TGYFWO2qpjizaUmEqBZ7yPkJT3mI/eMHdBnSoYDBsJEVNBCB1khR7Za7VvkaoQbLSIiSBwi 7dQ0SBrrPcqY8EuLEeAiw5Q80rGaEwIWpEmr123jOhgbT75ykZMjIQYuKFxYhgUNHJFI/CFdWg8M 06dQnwKlMAYoqahYg2gMSeLmi55ZwwLAtk2s2VkKnDGywbat27dw48oYEQFDTq88z55lQKBCBgMR COodTDdANTRlCStezLix48eCnPiCTJicJ7WUsbr7mHmxBLCdsaYrrOtqaJF+2Zxxmfi0SD8APk/D 7PpOhF8I2Sx0WNsLX4UJPIaj1rse0BfCZDd5YqF4IU84ARwXShRpCAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0040.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
To check if it is factorable;  a =3D 3,  b =3D -2,  c =3D -2
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0040_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAB7 ACgAhAAAAAAAAA0LCwUAAAUICwsICAsLDQUABQsFBQgIDQgFAAgFBQ0IBQAFCAUIDQAFCwgIBQsI BQsFAAUFCwAABQ0ICAsIDQsLCwUFBQUFCAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquYuC+ cCzPdF2zeK7rwe7/wKBw1Rsaj8hkESUYBAjJqDS6PBUMgoNhyu36qilEwkvGCRRP5mKLK57TpiuQ 0WCXh2K1nUjKlxgOQE11d0NZeyQCazlLh38PQQgQhIVBDJB6bSSXJREvgTuAEZSVPxIETpQSM5go VaepiD4CEwCje54Uk1tvAaClTRRYA78iirInjQPCTcU/CFu3xgqQTVAVxLZQUasyrZwAZ87HyVVL 4OIq3TGYFWO2qpjizaUmEqBZ7yPkJT3mI/eMHdBnSoYDBsJEVNBCB1khR7Za7VvkaoQbLSIiSBwi 7dQ0SBrrPcqY8EuLEeAiw5Q80rGaEwIWpEmr123jOhgbT75ykZMjIQYuKFxYhgUNHJFI/CFdWg8M 06dQnwKlMAYoqahYg2gMSeLmi55ZwwLAtk2s2VkKnDGywbat27dw48oYEQFDTq88z55lQKBCBgMR COodTDdANTRlCStezLix48eCnPiCTJicJ7WUsbr7mHmxBLCdsaYrrOtqaJF+2Zxxmfi0SD8APk/D 7PpOhF8I2Sx0WNsLX4UJPIaj1rse0BfCZDd5YqF4IU84ARwXShRpCAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0041.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
To check if it is factorable;  a =3D 3,  b =3D -2,  c =3D -2
So b2 – 4ac =3D (-2)2 – 4(3)(-2) =3D = 28
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0041_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAB7 ACgAhAAAAAAAAA0LCwUAAAUICwsICAsLDQUABQsFBQgIDQgFAAgFBQ0IBQAFCAUIDQAFCwgIBQsI BQsFAAUFCwAABQ0ICAsIDQsLCwUFBQUFCAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquYuC+ cCzPdF2zeK7rwe7/wKBw1Rsaj8hkESUYBAjJqDS6PBUMgoNhyu36qilEwkvGCRRP5mKLK57TpiuQ 0WCXh2K1nUjKlxgOQE11d0NZeyQCazlLh38PQQgQhIVBDJB6bSSXJREvgTuAEZSVPxIETpQSM5go VaepiD4CEwCje54Uk1tvAaClTRRYA78iirInjQPCTcU/CFu3xgqQTVAVxLZQUasyrZwAZ87HyVVL 4OIq3TGYFWO2qpjizaUmEqBZ7yPkJT3mI/eMHdBnSoYDBsJEVNBCB1khR7Za7VvkaoQbLSIiSBwi 7dQ0SBrrPcqY8EuLEeAiw5Q80rGaEwIWpEmr123jOhgbT75ykZMjIQYuKFxYhgUNHJFI/CFdWg8M 06dQnwKlMAYoqahYg2gMSeLmi55ZwwLAtk2s2VkKnDGywbat27dw48oYEQFDTq88z55lQKBCBgMR COodTDdANTRlCStezLix48eCnPiCTJicJ7WUsbr7mHmxBLCdsaYrrOtqaJF+2Zxxmfi0SD8APk/D 7PpOhF8I2Sx0WNsLX4UJPIaj1rse0BfCZDd5YqF4IU84ARwXShRpCAA7 ------=_NextPart_01C82DF5.41D86FC0 Content-Location: file:///C:/09764A33/1Solving2ndDegreeEquations_files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving 2nd Degree Equations
Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
To check if it is factorable;  a =3D 3,  b =3D -2,  c =3D -2
So b2 – 4ac =3D (-2)2 – 4(3)(-2) =3D = 28.    Not factorable!
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
To check if it is factorable;  a =3D 3,  b =3D -2,  c =3D -2
So b2 – 4ac =3D (-2)2 – 4(3)(-2) =3D = 28.    Not factorable!
Use QF, we get:
        = ;            &n= bsp;   
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
To check if it is factorable;  a =3D 3,  b =3D -2,  c =3D -2
So b2 – 4ac =3D (-2)2 – 4(3)(-2) =3D = 28.    Not factorable!
Use QF, we get:
        = ;            &n= bsp;   
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
To check if it is factorable;  a =3D 3,  b =3D -2,  c =3D -2
So b2 – 4ac =3D (-2)2 – 4(3)(-2) =3D = 28.    Not factorable!
Use QF, we get:
        = ;            &n= bsp;   
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=
Example:  Solve 3x2 – 2x – 2 = =3D 0
To check if it is factorable;  a =3D 3,  b =3D -2,  c =3D -2
So b2 – 4ac =3D (-2)2 – 4(3)(-2) =3D = 28.    Not factorable!
Use QF, we get:
        = ;            &n= bsp;   
Solving 2nd Degree Equations: ax2 + bx + c =3D 0
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Use the quadratic formula (QF): <= /span>
The roots for the equation ax<= span lang=3DEN-US style=3D'font-size:66%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>2 + bx + c =3D 0
are           = ;           .=