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Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when...
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Transcript of Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when...
![Page 1: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/1.jpg)
Using the Quadratic Formula to Find the Rootsy = 3x2 – 6x – 20 The roots are the x values when y = 0
-5
-10
-15
-20
-25
-30
5
-1-2-3-4 1 2 3 4 50X->
|̂Y
Y=3x̂ 2 - 6x- 20
x y-3 25-2 4-1 -110 -201 -232 -203 -114 45 25
From the table you can see that the y values change sign between –2 and –1 and between 3 and 4So the roots lie between –2 and –1 and between 3 and 4
Use your calculator to make a table of values using y = 3x2 – 6x – 20 and the TABLE key
![Page 2: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/2.jpg)
Using the Quadratic Formula to Find the Rootsy = 3x2 – 6x – 20 The roots are the x values when y = 0
a = 3 b = –6 c = –20
-5
-10
-15
-20
-25
-30
5
-1-2-3-4 1 2 3 4 50X->
|̂Y
Y=3x̂ 2 - 6x- 20
The Quadratic formula is used to find the roots
You can check this using x intercept on the CALC menu
![Page 3: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/3.jpg)
Using the Quadratic Formula to Find the Rootsy = 2x2 + 3x – 12 The roots are the x values when y = 0
2x2 + 3x – 12a = 2 b = 3 c = –12
The Quadratic formula is used to find the roots
You can check this using x intercept on the CALC menu
-5
-10
-15
5
-1-2-3-4 1 2 3 4 50X->
|̂Y
Y=2x̂ 2+3x- 12
![Page 4: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/4.jpg)
![Page 5: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/5.jpg)
![Page 6: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/6.jpg)
![Page 7: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/7.jpg)
![Page 8: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/8.jpg)
![Page 9: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/9.jpg)
![Page 10: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/10.jpg)
![Page 11: Using the Quadratic Formula to Find the Roots y = 3x 2 – 6x – 20 The roots are the x values when y = 0 xy -325 -24 -1-11 0-20 1-23 2-20 3-114 525 From.](https://reader036.fdocuments.us/reader036/viewer/2022081520/56649edb5503460f94bebdb0/html5/thumbnails/11.jpg)