Question

Determine an equation for the pictured graph. Write your answer in factored form and assume the leading coefficient is either or , you should be able to determine which is the case by looking at the graph. 1 2 3 -1 -2 -3 1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6 -7 -8 -9 Incorrect

Answer 1

The equation of the polynomial graphed is

f (x) = - x (x + 2) (x - 1)²

How to find the equation

The equation of the polynomial is solved using the formula

f (x) = a (x - p) (x - q) (x - r).....

Where p, q, r, ... are the roots of the equation

From the graph the roots are x = -2, x = 0, x = 1, twice

In factored form we have

f (x) = a x (x + 2) (x - 1)²

To solve for a we use point (-1, 4)

4 = a (-1) (-1 + 2) (-1 - 1)²

4 = a (-1) (1) ( -2)²

4 = -4a

a = -1

So the equation of the polynomial is

f (x) = - x (x + 2) (x - 1)²

Answer 2

The equation of the function represented by the graph in factored form is f(x) = -1/18(x + 3)²(x - 2)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 = -3 and 2

The zeros 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) = a(x + 3)²(x - 2)²

Using the point (0, -2) to calculate the leading coefficient a, we have

a(0 + 3)²(0 - 2)² = -2

36a = -2

Divide

a = -1/18

So, we have

f(x) = -1/18(x + 3)²(x - 2)²

Hence, the function in factored form is f(x) = -1/18(x + 3)²(x - 2)²

Question

Determine an equation for the pictured graph. Write your answer in factored form and assume the leading coefficient is either or , you should be able to determine which is the case by looking at the graph