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.

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

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

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

3. 2(12g² - g) = 15

4. 3x² + 5x +11

Discriminant: To find the number and types of roots of a quadratic equation use b² - 4ac x = b² - 4ac > 0; 2 real roots positive b² - 4ac = 0; 1 real root b² - 4ac < 0; no real roots negative

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

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