<PRE><B>Question 136931</B>
Hi,

The most he can earn is basically the maximum value of the function.
And the maximum occurs at the vertex of this parabola.

The given equation is P(x) = -x^2+12x+46,

The x coordinate of the vertex = {{{(-b)/(2*a)}}}

                               = {{{(-12)/(2*(-1))}}}

                               = 6

Plugging this value of x in P(x), P(6)= -36 + 72 + 46
                                      = 82

Thus the most he can earn is 82 

Good luck!!!

dolly

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