Math worksheet

Write and Graph Polynomial Functions

Learning Objectives

· Draw conclusions about a polynomial function from a graph

· Graph polynomial functions

· Write a formula for a polynomial function from a graph

· Determine equation of a polynomial given key information

Draw conclusions about a polynomial function from a graph

1. Given the graph below, what can be concluded about the polynomial function based on the intercepts and turning points?

2. Given the graph below, what can be concluded about the polynomial function based on the intercepts and turning points?

Graph polynomial functions

3. Graph .

4. Graph .

Write a formula for a polynomial function from a graph

5. Write a formula for the polynomial function given the graph below.

6. Write a formula for the polynomial function given the graph below.

Determine equation of a polynomial given key information

7. Find the equation of a polynomial of degree 4 with zeros at and , and

y-intercept .

8. Find the equation of a polynomial of degree 4 with zeros at and , and

y-intercept .

ANSWER KEY

1. The graph has 3 x-intercepts, which suggests that a function has degree 4 or greater. It also has 3 turning points, which suggests that a function has degree of 4 or greater. So it can be concluded that the function is even and has degree of 4 or greater.

2. The graph has 2 x-intercepts and 2 turning points. Also the two ends of the function are going in opposite directions. So the polynomial has a degree of 3 or greater and is an odd function.

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