Express $f ( x )$ In the Form $a _ { n } x ^ { n } + a _ { n - 1 } x ^ { n - 1 } + \ldots + a _ { 1 } x + a _ { 0 }$

Multiple Choice

Express $f ( x )$ in the form $a _ { n } x ^ { n } + a _ { n - 1 } x ^ { n - 1 } + \ldots + a _ { 1 } x + a _ { 0 }$ . Find a quadratic function that has a maximum value of 2 and that has - 2 and 4 as zeros.

A) $f ( x ) = - \frac { 4 } { 9 } x ^ { 2 } + \frac { 2 } { 9 } x - \frac { 16 } { 9 }$
B) $f ( x ) = - \frac { 9 } { 2 } x ^ { 2 } - \frac { 16 } { 9 } x + \frac { 4 } { 9 }$
C) $f ( x ) = - \frac { 2 } { 9 } x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 16 } { 9 }$
D) $f ( x ) = \frac { 2 } { 9 } x ^ { 2 } - \frac { 9 } { 4 } x - \frac { 16 } { 9 }$