Graphing Polynomials Worksheet

Graphing Polynomials

Read each question carefully and provide complete answers. Show all your work for full credit. Sketch graphs neatly on the provided coordinate planes.

1. Consider the polynomial function P(x) = (x + 2)(x - 1)^2(x - 3).

a) Determine the degree of the polynomial.

b) List the x-intercepts and their multiplicities.

c) Describe the end behavior of the graph of P(x).

2. Sketch the graph of the polynomial function f(x) = -x^3 + 4x^2 - 4x.

a) Find the x-intercepts and y-intercept.

b) Determine the end behavior of the graph.

c) Create a sign chart for f(x).

d) Sketch the graph of f(x) on the coordinate plane below.

3. For a polynomial function of odd degree, the graph must cross the x-axis at least once.

4. Which of the following polynomial functions has a graph that rises to the left and falls to the right?

5. If a polynomial function has a root with an even multiplicity, its graph will   the x-axis at that intercept.

6. The maximum number of turning points a polynomial of degree 'n' can have is  .

7. A polynomial function has x-intercepts at -3 (multiplicity 1), 0 (multiplicity 2), and 2 (multiplicity 1). Its y-intercept is (0,0). The leading coefficient is positive. Sketch a possible graph of this function.