1. 9-2A Solving Quadratic Equations by Graphing One One way to solve a quadratic equation is to graph the equation. Algebra 1 Glencoe McGraw-HillLinda Stamper and JoAnn Evans

2. The x-intercepts of the graph are the solutions, or roots, of the related equation Because at the x-intercept, y is equal to 0. function related equation Notice the first equation is equal to y and the second equation is equal to 0. Why is y = 0?

3. x y The x-intercepts are –2 and 2 thus the solutions, or roots, are –2 and 2. x y The x-intercepts are –4 and 1 thus the solutions, or roots, are –4 and 1. The solutions, or roots, are NOT ordered pairs.

4. If the vertex of the parabola is on the x-axis, there is one solution. It is the x-coordinate of the vertex. If the parabola does not intersect the x-axis, then there is no real solution. x y There is one solution, or root: –1. x y There is no real solution. The solution, or root, is NOT an ordered pair. There is one solution, or root: 2.

5. Example 1 The graph of is shown. Use the graph to estimate the solutions of Check your solutions algebraically. Check x y The solutions, or roots, are –3 and 3.

6. Remember to choose values to the left and right of the vertex or you will not graph a parabola. Estimating Solutions By Graphing 1. Write the equation in standard form 2. Sketch the graph of the related quadratic function (Find the vertex and set up a table of values. You may need to use more than 5 values.) 3. Estimate the values of the x-intercepts, if any. 4. Check the solution/s algebraically – in the original equation.

7. Use a graph to estimate the solutions of x 2 + x = 12. Check your solution/s algebraically Rewrite the equation in standard form. Write the related function. Find the x-coordinate of the vertex. Write the equation – use the original equation to check your solutions.

8. x y 0 1 -2 y-intercept -10 matchy, matchy ! -12 -10

9. x y You may need to calculate more coordinates! x y 0 1 -2 y-intercept -10 matchy, matchy ! -12 -10

11. x y Estimate the solutions. –4,and 3 x y 2 3 -3 -4 y-intercept 0 matchy, matchy ! -6 0

12. Check – be sure to use the original equation. –4 and 3

13. Example 3 Example 4 Example 5 Use a graph to estimate the solutions of the equations. Check your solution/s algebraically. Example 2 Rewrite the equation in standard form. Write the related function. Sketch graph of function. Find the x-coordinate of the vertex and complete a table of values. Plot points. Write the given equation. Check the solution/s algebraically – in the original equation.

14. x y 3 4 1 0 y-intercept -5 matchy, matchy ! -8 -5 Example 2

15. x y You may need to calculate more coordinates! Estimate the solutions. You must check your solutions! x y 3 4 1 0 y-intercept -5 matchy, matchy ! -8 -5

16. 0 1 2 3 Example 3 Sketch the graph of: x y 0 -3 -4 -3 0 matchy, matchy !

17. Example 4 Sketch the graph of: -2 0 1 2 x y -3 0 1 0 -3 matchy, matchy !

18. Example 5 Sketch the graph of: 1 2 3 4 5 x y 3 0 0 3 matchy, matchy !

19. 9-A3 Handout A3. Don’t forget to check your solution/s algebraically.