Question

The owner of a video game store creates the expression −2x2 + 24x + 174 to represent the store's weekly profit in dollars, where x represents the price of a new video game. Choose the equivalent expression that reveals the video game price that produces the highest weekly profit, and use it to determine the price.

−2(x2 − 12x) + 174; x = $12
−2(x2 − 12x − 87); x = $87
−2(x − 6)2 + 246; x = $246
−2(x − 6)2 + 246; x = $6

Answer 1

-2(x-6)^2+246; x=$6

Hope it helps!

Answer 2

`-2(x-6)^2+246`, x = $6

Explanation:

The expression
`-2x^2+24x+174` to represent the store's weekly profit in dollars, where x represents the price of a new video game.

Let
`f(x)=-2x^2+24x+174`

We need to rewrite this quadratic function in the vertex form.

`f(x)=-2(x^2-12x)+174`

`f(x)=-2(x^2-12x+36)--2(36)+174`

`f(x)=-2(x^2-12x+36)+72+174`

`f(x)=-2(x-6)^2+246`

The equivalent expression that reveals the video game price that produces the highest weekly profit is
`-2(x-6)^2+246`

and the price is $6