Question

construct a polynomial function with the stated properties. third degree with zeros of -2,-1, and 3 and passes through the point (2,12)

Answer 1

Answer:

$f(x) = - (x + 2)(x + 1)(x - 3)$

Step-by-step explanation:

Let f(x) be the 3rd degree polynomial function.

The roots of this function are:

x=-2, x=-1 and x=3.

The factored form is:

$f(x) = a(x + 2)(x + 1)(x - 3)$

This equation passes through (2,12)

This implies that;

$a(2 + 2)(2+ 1)(2 - 3) = 12 \\ - 12a = 12 \\ a = - 1$

The polynomial function is

$f(x) = - (x + 2)(x + 1)(x - 3)$