Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make
the degree of the function as small as possible.
-Crosses the $x$-axis at $- 2,0$, and 4 ; lies below the $x$-axis between $- 2$ and 0 ; lies above the $x$-axis between 0 and 4 .
A) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x$
B) $f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 8 x$
C) $f ( x ) = - x ^ { 3 } - 2 x ^ { 2 } + 8 x$
D) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 8 x$

Question

Quizplus · Accepted Answer

The polynomial must have roots at -2, 0, and 4. The function should be negative between -2 and 0 and positive between 0 and 4, which is achieved by a cubic polynomial with a negative leading coefficient.

Write the Equation of a Polynomial Function with the Given xxx

Write the Equation of a Polynomial Function with the Given $x$