Graphing of Polynomial Function.pptx

This topic will help the students on how to graph a polynomial function in step-by-step process.

1. Graphing of polynomial function

2. Turning point -the turning points of a graph occur when the function is changing values, from decreasing to increasing or from increasing to decreasing. A polynomial function of degree n has n-1 turning points on its graph or the number of turning points is always less than the degree n .

3. multiplicity -the multiplicity of root r is the number of times that x-r is a factor of P(x ). When a real root has even multiplicity , the graph of f(x) is tangent to the x-axis. When a real root has odd multiplicity greater than 1, the graph bends as it crosses the x-axis.

4. STEPS ON GRAPHING POLYNOMIAL FUNCTION STEP 1: Determine the end behavior and number of turning point of the graph. STEP 2: Factor the polynomial function.

5. STEPS ON GRAPHING POLYNOMIAL FUNCTION STEP 3: Find the x- and y-intercept of the polynomial function STEP 4: Make a table of values STEP 5: Plot the points and sketch the graph of the polynomial function.

6. Example y = x 2 – x – 2 y = (x + 1)(x – 2) y = x 3 + 3x 2 – x – 3 y = (x + 1)(x – 1)(x + 3)

7. Example f(x) = -x 4 – 5x 3 – 5x 2 + 5x + 6 f(x) = (x + 1)(x – 1)(x + 2)(-x – 3)

8. Example y = x 5 + 4x 4 + x 3 – 10x 2 – 4x + 8 y = (x + 2) 3 (x – 1) 2

9. Try this y = x 3 – 5x 2 + 2x + 8 y=x 5 + 3x 4 – 6x 3 – 10x 2 + 21x – 9