Solving Quadratic Functions by Graphing

To solve by graphing… Take your function and write it in standard form. Instead of making it y = blah, blah, blah, make it 0 = blah, blah, blah Enter the blah, blah, blah part in f1 Enter the 0 in f2 Use menu > 6: Analyze Graph > 4: Intersection Lower bound and upper bound should surround the x-intercepts

Example 1 Solve:2x 2 – 2 = 0 Enter 2x 2 – 2 in f1 Enter 0 in f2 Graph. Go to Menu > Analyze Graph > Intersection The line for lower bound should be to the left of the x intercept. Enter. The line for upper bound should be to the right of the x intercept. Enter. The x is one of the solutions.

Example 1 cont. To find the other one, Menu> Analyze Graph > Intersection The line for lower bound should be to the left of the other x intercept. Enter. The line for lower bound should be to the right of the other x intercept. Enter Solutions 1 or -1 x = 1 or -1

Example 2 Solve:x = 4x Put in standard form:x 2 - 4x + 5 = 0 Enter x 2 – 4x + 5 in f1 Enter 0 in f2 Graph Notice that this never crosses the x- axis, so there will be no zeroes. No solution.

Example 3 Solve:-x 2 - 4x – 4 = 0 Enter –x 2 – 4x – 4 in f1 Enter 0 in f2. Graph Find the intersection. It only crosses the x-axis once, so there is only one solution. x = -2

Estimate the roots of each quadratic function represented below. XY XY

Try these… x 2 – 8x – 16 = 2x 2 6x + 10 = -x 2 -x = 0 x = -4 No solution x = -2 or 2