Question

Writing a Polynomial Function Given a y-Intercept:

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5).
Describe the steps for writing the equation of this cubic polynomial function.

Answer 1

Use the zeroes to determine the roots.

Write the polynomial as a product of the leading coefficient, a, and the factors, where each factor is x minus a root.

Use the y-intercept (0, –5) to solve for the leading coefficient.

Substitute the leading coefficient into the polynomial function for a and simplify.

Explanation:

Answer 2

We are given

a cubic polynomial function has the same zeroes

Let's assume that zeros as 'a'

so, we can write it as

`f(x)=(x-a)^3`

now, we are given y-intercept

(0,-5)

at x=0 , y=-5

we can use it and then find 'a'

`-5=(0-a)^3`

`a=\sqrt[3]{5}`

now, we can plug it

and we get

`f(x)=(x-\sqrt[3]{5})^3`..................Answer