1. 4.6 Quadratic formula

2. Concept

3. Example 1 Solve x2 – 8x = 33 by using the Quadratic Formula.
Two Rational Roots
Solve x2 – 8x = 33 by using the Quadratic Formula.
First, write the equation in the form ax2 + bx + c = 0 and identify a, b, and c.
x2 – 8x = 33 1x2 – 8x – 33 = 0
Then, substitute these values into the Quadratic Formula.
Quadratic Formula

4. Solve x2 + 13x = 30 by using the Quadratic Formula.

5. Example 2 Solve x2 – 34x + 289 = 0 by using the Quadratic Formula.
One Rational Root
Solve x2 – 34x = 0 by using the Quadratic Formula.

6. Example 3 Solve x2 – 6x + 2 = 0 by using the Quadratic Formula.
Irrational Roots
Solve x2 – 6x + 2 = 0 by using the Quadratic Formula.

7. Example 4 Solve x2 + 13 = 6x by using the Quadratic Formula.
Complex Roots
Solve x = 6x by using the Quadratic Formula.

8. Solve x2 + 5 = 4x by using the Quadratic Formula.

9. Concept

10. Example 5
Describe Roots
A. Find the value of the discriminant for x2 + 3x + 5 = 0. Then describe the number and type of roots for the equation.

11. Example 5
Describe Roots
B. Find the value of the discriminant for x2 – 11x + 10 = 0. Then describe the number and type of roots for the equation.

12. Give the values of b for which the equation has two real solutions
3x2 + bx + 27=0

13. Concept