Question

I need help with this word problem but only with the question "e"

Answer 1

Part e

we have the function

`P(x)=-2x^2+32x-110`

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

`P(x)=-2(x^2-16x)-110`

step 2

Complete the square

`\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}`

step 3

Rewrite as perfect squares

`P(x)=-2(x-8)^2+18`

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