Question

In the xy-plane, the graph of function f(x) has zeros at −5, −2, and 2. Write the polynomial function.

Answer 1

Answer:

$f(x) = x^3 +5x^2-4x-20$

Step-by-step explanation:

Given

$Zeros: -5,-2,2$

Required

The polynomial function

If a function has a, b and c as its zeros, the function is:

$f(x) = (x - a)(x - b)(x - c)$

So, we have:

$Zeros: -5,-2,2$

$f(x) = (x - (-5))(x - (-2))(x - 2)$

Open the inner brackets

$f(x) = (x +5)(x +2)(x - 2)$

Expand the difference of two squares

$f(x) = (x +5)(x^2 - 4)$

Expand

$f(x) = x^3 +5x^2-4x-20$