Question

A cubic equation hasczeros at -2, 1, and 3 a) Write an eqn for a polynomial function that meets the given conditions.b) Draw the graph oh a polynomial function that meets the given conditions.

Answer 1

The zeros of a cubic function are -2, 1, and 3.

(a)

The simplest way to construct an equation that has a, b, and c as its zeros is:

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

From the problem, we identify:

$\begin{gathered} a=-2 \\ b=1 \\ c=3 \end{gathered}$

Then:

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

(b)

The graph of the function is: