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

Multiple Choice

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) $f ( x ) = - x ^ { 3 } + 4 x ^ { 2 }$