Question

Determine an equation for the pictured graph. Write your answer in factored form and assume the leading

coefficient is either 1 or -1, you should be able to determine which is the case by looking at the graph.

Answer 1

The equation of the function represented by the graph in factored form is f(x) = -x²(x + 2)²(x - 1)²

How to determine the function in factored form

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

Zeros: x = -2 and 0 and 1

The zeros -2 and 0 have a multiplicity of 2 each

This is so because the graph turns at these points on the x-axie

So, we have the expression in factored form to be

f(x) = (x + 2)²(x - 0)²(x - 1)²

The graph opens down

So, we have

f(x) = -(x + 2)²(x - 0)²(x - 1)²

Evaluate

f(x) = -x²(x + 2)²(x - 1)²

Hence, the function in factored form is f(x) = -x²(x + 2)²(x - 1)²