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

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

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-20

-25

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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

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