Find Constants A, B, and C So That the Graph $f ( x ) = a x ^ { 2 } + b x + c$

Multiple Choice

Find constants a, b, and c so that the graph of the function $f ( x ) = a x ^ { 2 } + b x + c$ 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