# Precalculus : Graphs of Polynomial Functions

## Example Questions

2 Next →

### Example Question #3 : Write The Equation Of A Polynomial Function Based On Its Graph

Write the quadratic function for the graph: Possible Answers:     Correct answer: Explanation:

Method 1:

The x-intercepts are .  These values would be obtained if the original quadratic were factored, or reverse-FOILed and the factors were set equal to zero.

For , .  For , .  These equations determine the resulting factors and the resulting function; .

Multiplying the factors and simplifying, .

Answer: .

Method 2:

Use the form , where is the vertex. is , so , . Answer:    ### Example Question #4 : Write The Equation Of A Polynomial Function Based On Its Graph

Write the equation for the polynomial in this graph: Possible Answers:     Correct answer: Explanation:

The zeros for this polynomial are .

This means that the factors are equal to zero when these values are plugged in for x. multiply both sides by 2 so one factor is  multiply both sides by 3 so one factor is  so one factor is Multiply these three factors:   ### Example Question #5 : Write The Equation Of A Polynomial Function Based On Its Graph

Write the equation for the polynomial shown in this graph: Possible Answers:     Correct answer: Explanation:

The zeros of this polynomial are . This means that the factors equal zero when these values are plugged in.

One factor is One factor is The third factor is equivalent to . Set equal to 0 and multiply by 2:  Multiply these three factors:  The graph is negative since it goes down then up then down, so we have to switch all of the signs: ### Example Question #6 : Write The Equation Of A Polynomial Function Based On Its Graph

Write the equation for the polynomial in the graph: Possible Answers:     Correct answer: Explanation:

The zeros of the polynomial are . That means that the factors equal zero when these values are plugged in.

The first factor is or equivalently multiply both sides by 5: The second and third factors are and Multiply:   Because the graph goes down-up-down instead of the standard up-down-up, the graph is negative, so change all of the signs: ### Example Question #7 : Write The Equation Of A Polynomial Function Based On Its Graph

Write the equation for the polynomial in this graph: Possible Answers:     Correct answer: Explanation:

The zeros for this polynomial are . That means that the factors are equal to zero when these values are plugged in. or equivalently multiply both sides by 4 the first factor is  multiply both sides by 3 the second factor is  the third factor is Multiply the three factors:   2 Next →

### All Precalculus Resources 