Part e
we have the function
[tex]P(x)=-2x^2+32x-110[/tex]
The given function represents a vertical parabola, open downward
The vertex represents a maximum
so
Convert the given equation into vertex form
step 1
Factor -2
[tex]P(x)=-2(x^2-16x)-110[/tex]
step 2
Complete the square
[tex]\begin{gathered} P(x)=-2(x^2-16x+64-64)-110 \\ P(x)=-2(x^2-16x+64)-110+128 \\ P(x)=-2(x^2-16x+64)+18 \end{gathered}[/tex]
step 3
Rewrite as perfect squares
[tex]P(x)=-2(x-8)^2+18[/tex]
The vertex is the point (8,18)
That means
8 is the number of games in hundreds -------> 800 games
18 is the profit in ten thousand ------> 18*10,000=$180,000
so
The maximum profit is $180,000 for 800 games
