1. Warm-Up 2.10
Solve the following.
8x2 + 18x + 9 = 0
Answers: x = or x = -0.75

2. Teacher (Magnani)
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
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
Enter the equation into y= (top left button)
Hit Graph (top right button)
Go to 2nd Trace
Choose #2 – Zeros
Scroll cursor over until it is sitting on the far left x-intercept
Hit the LEFT Arrow key twice
Hit enter
Move the cursor back to the x-intercept it was just on
Hit the RIGHT Arrow key twice
Hit Enter
Hit Enter when it says Guess
The x-value that appears is one of the solutions
Continue on Next Slide

6. Finding the x-intercepts (zeros) in the Calculator
Hit 2nd Trace
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.
x2 – x – 12 = 0
Answers: x = -3 and x = 4

8. Examples: Solve each equation through graphing. 3x2 – 2x – 8 = 0
Teacher (Magnani)
Examples: Solve each equation through graphing.
3x2 – 2x – 8 = 0 .
Answers: x = and x = 2

9. Examples: Solve each equation through graphing.
x2 – 14x = 15
8x2 – 14x – 15 = 0
Answers: x = 2.5 and x = -0.75

10. Examples: Solve each equation through graphing.
x = -7x
-5x2 + 7x + 14 = 0
Answers: x = and x = 2.51

11. Examples: Solve each equation through graphing.
x2 + 4x + 6 = 0
Answers: No Real Solution

12. Complete Worksheet 2.10