Solve the problem
-John owns a hotdog stand. His profit is represented by the equation $\mathrm { P } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 12 \mathrm { x } + 45$, with $\mathrm { P }$ being profits and $x$ the number of hotdogs sold. What is the most he can earn?
A) $81
B) $117
C) $63
D) $36

Question

Quizplus · Accepted Answer

The profit function is a parabola with a maximum at the vertex. The x-coordinate of the vertex is -b/2a = -12/(-2) = 6. So, the most John can earn is P(6) = -6^2 + 12(6) + 45 = $81.

Solve the Problem -John Owns a Hotdog Stand P(x)=−x2+12x+45\mathrm { P } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 12 \mathrm { x } + 45P(x)=−x2+12x+45

Solve the Problem
-John Owns a Hotdog Stand $\mathrm { P } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 12 \mathrm { x } + 45$