3. Algebra 3 Lesson 2.6 Objective: SSBAT solve quadratic equations. Standards: M11.D.2.1.5

4. Solving Equations  Finding all of the values for the variable that will make the equation true

5. Solving Quadratic Equations may also be referred to as finding the ZEROS of the function or finding the ROOTS of the function. Methods: Factoring Taking Square Root of Both Sides Quadratic Formula Completing the Square Graphing

6. Solving Quadratic Equations by Factoring 1.Set the equation equal to zero (get everything on the same side) 2.Factor the expression 3.Set each factor equal to zero 4.Solve each equation

7. Solve each equation. 1. 3x 2 – x – 10 = 0 (3x + 5)(x – 2) = 0 3x + 5 = 0 or x – 2 = 0 x = 2

8. Solve each equation. 2.2x 2 + 11x = 6 2x 2 + 11x – 6 = 0 (2x - 1)(x + 6) = 0 2x – 1 = 0 or x + 6 = 0 x = -6

9. Solve each equation. 3. x 2 + 16 = 17x x 2 – 17x + 16 = 0 (x – 1)(x – 16) = 0 x – 1 = 0 or x – 16 = 0 x = 1 x = 16 Answers: x = 1 and x = 16

10. Solve each equation. 4. 2x 2 = 7x + 15 2x 2 – 7x – 15 = 0 (2x + 3)(x – 5) = 0 2x + 3 = 0 or x – 5 = 0 x = 5

11. 5. 16x 2 – 5x = 0 x(16x – 5) = 0 x = 0 or 16x – 5 = 0 16x = 5 x = 0.3125

12. Answer: C

13. Solving Quadratic Equations of the form x 2 - # = 0 1.Isolate the x 2 term 2. Take the square root of both sides 3. Remember the ±

14. or x = 8 and -8

18. On Your Own Solve. x 2 – 5x – 14 = 0 Answer: x = 7 or x = -2

19. Homework Worksheet 2.6