1. Lesson 10.4: Solving Quadratic Equations Using the Quadratic Formula, pg. 546
Goals:
To solve quadratic equations by using the Quadratic Formula.
To use the discriminant to determine the number and type of roots of a quadratic equation.

2. Quadratic Formula
The solutions of a quadratic equation of the form ax² + bx + c = 0, where a ≠ 0, are given by the following formula.
To solve quadratic equations using the quadratic formula, the equation must be set equal to ZERO

3. Example 1: Solve by using the quadratic formula.
1. x² - 2x – 35 = 0

4. Round to the nearest tenth if necessary.
2. 15x² - 8x = 4

5. 3. 2(12g² - g) = 15

6. 4. 3x² + 5x +11

7. Discriminant: To find the number and types of roots of a quadratic equation use b² - 4ac
x =
b² - 4ac > 0; real roots
positive
b² - 4ac = 0; real root
b² - 4ac < 0; no real roots
negative

8. Ex. 2: Describe the roots using the discriminant.
1. 4x² - 2x + 14 = 0
2. x² + 24x = -144

9. 3. 3x² + 10x = 12
4. x² - 11x + 10 = 0