1. 5.8 SUMMARY OF ZEROS, FACTORS, SOLUTIONS AND INTERCEPTS FINDING THE TURNING POINTS. SWBAT USE INTERCEPTS TO GRAPH FUNCTIONS

2. 5.8 A Summary of zeros, factors, solutions, and intercepts. If K is a zero of f(x), then x - k is a factor, k is a solution and if k is a real number, then k is a x-intercept of the graph of f(x) and passes through (k, 0).

3. Finding the low turning point first, 2 nd TRACE, (or calc), arrow down to minimum Bottom left of screen, asks LeftBound?, using the left and right arrow keys, move the cursor to the immediate left of the min., enter. Bottom left of screen, asks, RightBound, using the left and right arrow keys, move the cursor to the immediate right of min. enter. Bottom left of screen, asks, Guess?, move cursor as close as possible to the min. and enter, the minimum, point should be on the graph. Use the same technique to find the local maximum.

4. Moving left to right, local max: (-1.62, 5.85) local min: (-.29, -4.63) local max: (1, 0) local min: (1.71, -1.47)

5. F(x) = Curious, did you notice in the two graphs that we just did, one of the turning points for each was on the x- axis, is there a significance to this? This means that, that zero happens twice in the polynomial.

6. Now, a fairly simply equation to graph.

7. Zeros are -2, -1, 1 Min: ( -2, 0) and (0.4, -4.8) Max: (-1.4, 0.3)

8. You are making a rectangular box out of a piece of cardboard that measures 12 inches by 15 inches. The box will be formed by making the cuts shown in the diagram and folding up the sides. You want the box to have the greatest volume possible. 12in. 15 in. x x x x x x x x How long should you make the cuts? What is the maximum volume? What will the dimensions of the finished box be? Local max: (2.21, 177.23) Greatest volume would be 177.23 cu in. if x(the cuts) = 2.2, Dimensions 10.6 x 7.6 x 2.2