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

Question

Quizplus · Accepted Answer

The function has a relative maximum at (7,34), which means the derivative of the function at x=7 gives 0, and since it crosses the y-axis at (0,6), c=6. Differentiating $f(x) = ax^2 + bx + c$ gives $f'(x) = 2ax + b$. Setting $f'(7) = 0$ and $f(0) = 6$ helps find a and b. The correct signs for a and b come from the fact that a relative maximum requires a < 0, and fitting the given points leads to the solution.

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