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.
-Touches the $x$-axis at 0 and crosses the $x$-axis at 4 ; lies above the $x$-axis between 0 and 4 .
A) $f ( x ) = x ^ { 3 } + 4 x ^ { 2 }$
B) $f ( x ) = x ^ { 3 } - 4 x ^ { 2 }$
C) $f ( x ) = - x ^ { 3 } - 4 x ^ { 2 }$
D) $f ( x ) = - x ^ { 3 } + 4 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The function must have a factor of $x$ to touch the $x$-axis at 0 and a factor of $(x-4)$ to cross the $x$-axis at 4. Since the function lies above the $x$-axis between 0 and 4, the leading coefficient must be negative. Therefore, the function must be $f(x) = -x(x-4) = -x^2 + 4x$.

Write the Equation of a Polynomial Function with the Given xxx

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