1. Warm-Up 2.10 Solve the following. 8x 2 + 18x + 9 = 0 Answers: x = -1.5 or x = -0.75

2. Algebra 3 Lesson 2.10 Objective: SSBAT solve a quadratic equations through graphing the equation and finding the x- intercepts. Standards: M11.D.4.1.1

3. Solving A Quadratic Equation  Find all the x-values that make the equation true. Also referred to as:  Finding the zeros/roots/x-intercepts X-Intercept  Point where the graph crosses the x-axis

4. Solving Quadratic Equations through Graphing 1.Make the equation equal to 0 (if it is not already) 2. Graph the equation 3. Find the x-intercepts 4. The solutions are the x-intercepts

5. Finding the x-intercepts (zeros) in the Calculator 1.Enter the equation into y= (top left button) 2.Hit Graph (top right button) 3.Go to 2 nd Trace 4.Choose #2 – Zeros 5.Scroll cursor over until it is sitting on the far left x-intercept 6.Hit the LEFT Arrow key twice 7.Hit enter 8.Move the cursor back to the x-intercept it was just on 9.Hit the RIGHT Arrow key twice 10.Hit Enter 11.Hit Enter when it says Guess 12.The x-value that appears is one of the solutions Continue on Next Slide

6. Finding the x-intercepts (zeros) in the Calculator 13. Hit 2 nd Trace 14. Number 2 15. Scroll cursor over until it is sitting on the far right x-intercept 14. Hit the LEFT Arrow key twice 15. Hit enter 16. Move the cursor back to the x-intercept it was just on 17. Hit the Right Arrow key twice 18. Hit Enter 19. Hit Enter when it says Guess 20. The x-value that appears is the other solution

7. Examples: Solve each equation through graphing. 1.x 2 – x – 12 = 0 Answers: x = -3 and x = 4

8. Examples: Solve each equation through graphing. 2. 3x 2 – 2x – 8 = 0. Answers: x = -1.33 and x = 2

9. Examples: Solve each equation through graphing. 3. 8x 2 – 14x = 15 8x 2 – 14x – 15 = 0 Answers: x = 2.5 and x = -0.75

10. Examples: Solve each equation through graphing. 4. -5x 2 + 14 = -7x -5x 2 + 7x + 14 = 0 Answers: x = -1.11 and x = 2.51

11. Examples: Solve each equation through graphing. 5. 3x 2 + 4x + 6 = 0 Answers: No Real Solution

12. Complete Worksheet 2.10