Study Guide
Solving Quadratics by Using the Quadratic Formula

The method of completing the square (Section 13-6) can be used to develop a general fromula called the quadratic formula that can be used to solve any quadratic function.
The expression under the radical, b2 - 4ac, is called the discriminant. In order for the roots (aka, positions where the parabola crosses the x-axis) of a quadratic function to be real, the discriminant must be non-negative. If the disciminant is negative, then the parabola NEVER crosses the x-axis.

Example: Use the quadratic formula to solve x2 − 6x − 2 = 0.

The ≈ tell you that the roots are approximately equal to the stated values.

1. 4t2 = 144

 

−6, 6

2. 2x2 + 9x + 4 = 0

 

−4, −½

3. 8x2 + 17x + 2 = 0

 

−2 −⅛

4. 3z2 + 5z −2 = 0

 

−2, ⅓

5. −2m2 + 8m + 4 = 0

 

4.45, −0.45

6. x2 + 3x - 2 = 0

 

0.56, −3.56

7. 2x2 −6x + 4 = 0

 

1, 2

8. 5x2 + 10 = 15

 

−1, 1

2y2 −9y −3 = 0

 

4.81, −0.31