john owns a hot dog stand. his profit in dollars is given by the equation P(x)=P=-x^2+14x+54, where x is the number of hot dogs sold. what is the most he can earn?

okay, that's an upside-down U and the maximum value is at the top

if you put the function in vertex form you can easily find the vertex:

group the first two terms and factor out the negative (essentially factoring out -1):

p = - (x²-14x) + 54

complete the square by taking the middle coefficient (14), dividing it by 2, squaring it and adding the result to the terms in parentheses

p = -(x²-14x+49) + 54 + 49 (we've really subtracted 49, so we have to undo this by adding 49)

p = -(x-7)² + 103

the vertex is at (7,103), so your maximum profit is **$103**

## Comments

is that really positive x²? your profit function is a quadratic function which opens up..that means it goes up to infinity.

sorry! you're correct ..its negative