Find Constants A,b,and C So That the Graph of the Function

Multiple Choice

Find constants a,b,and c so that the graph of the function $f ( x ) = c x ^ { 2 } + b x + c$ has a relative maximum at (7,34) and crosses the y-axis at (0,6) .

A) $a = \frac { 4 } { 7 }$ ,b = 8,c = 6
B) $a = - \frac { 4 } { 7 }$ ,b = -8,c = -6
C) $a = \frac { 4 } { 7 }$ ,b = -8,c = 6
D) $a = - \frac { 4 } { 7 }$ ,b = 8,c = 6