John owns a hotdog stand. His profit is represented by the equation $P ( x ) = - x ^ { 2 } + 14 x + 54$ with P being profits and x the number of hotdogs sold. What is the most he can earn?
A) $103
B) $75
C) $117
D) $49

Question

Quizplus · Accepted Answer

The equation is a parabola with a maximum at the vertex. The x-coordinate of the vertex is -b/2a = -14/2(-1) = 7. The profit at this point is P(7) = -7^2 + 14(7) + 54 = 103.

John Owns a Hotdog Stand P(x)=−x2+14x+54P ( x ) = - x ^ { 2 } + 14 x + 54P(x)=−x2+14x+54

John Owns a Hotdog Stand $P ( x ) = - x ^ { 2 } + 14 x + 54$