1. Solving Polynomial Equations – Graphing Method This presentation explains how to solve polynomial equations graphically. The first step is to get the polynomial equation into the following form: An example would be …

2. Let y1 equal the left side of the equation … … yielding …

3. … we have … Since the right side of the equation is zero …

4. Recall that anytime the y-value is zero, on the graph the ordered pair (x,0) is a point on the x-axis. (-3,0)(1,0) (5,0)

5. The solutions to the equation … … are the x-values for which y1 (left side of equation) is equal to zero, … or the x-values of the x-intercepts on the graph of y1.

6. Example 1: Use the graphing method to solve the polynomial equation: Simplify, with all non-zero terms on the left hand side.

7. Let y1 equal the left hand side and enter the result into the calculator. Press Zoom-6 to graph Since it appears that the intercepts may be integers, use the Trace method.

8. Press Trace and then enter -2. Now repeat the process with x = 2, the intercept on the right. Since the y-value is 0, (-2,0) is an x-intercept, and -2 is a solution to the equation. Again, the y-value is 0. The solutions to the equation are x = -2, 2

9. Example 2- non-integer answers: Use the graphing method to solve the quadratic equation. Round answers to the nearest thousandth: Simplify, with all terms on the left hand side.

10. Let y1 equal the left hand side and enter the result into the calculator. Press Zoom-6 to graph Try the Trace method to see if the intercepts are integers.

11. Press Trace and then the x-value on the left, -1. Since the y-value is not 0, (-1,0) is not an x-intercept. Enter y2 = 0, and graph. Notice that nothing has appeared to change. This is because y2 = 0 is right on the x-axis. Use the intersect method to find approximate x-intercepts.

12. Press 2 nd |Calc|Intersect. The calculator asks three questions. Speed up the process by doing the following. Use the left arrow key to move the cursor close to the intersection point on the left. Press the Enter key three times.

13. Notice that y = 0, and (-1.192582,0) is an approximate x-intercept. Go through the same process to find the other x-intercept. Use the right arrow to move the cursor to the right intercept … Press 2 nd |Calc|Intersect. Press the Enter key three times.

14. Here we find that y = 0, and (4.1925824,0) is an approximate x-intercept. The two intercepts are (-1.192582,0) and (4.1925824,0) Rounded to the nearest thousandth, the two solutions to the quadratic equation are: x ≈ -1.193, 4.193