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

Answer:

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

Step-by-step 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

Answer 2

Answer:

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

Hope it helps!