The owner of a video game store creates the expression −2x2 + 28x + 20 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 that price.

a. −2(x − 7)2 + 118; x = $7
b. −2(x − 7)2 + 118; x = $118
c. −2(x2 − 14x) + 20; x = $14
d. −2(x2 − 14x − 10); x = $10

A. −2(x − 7)2 + 118; x = $7

Step-by-step explanation:

The expression −2x² + 28x + 20 represent the store weekly profit in dollars, where x represents the price of a new video game.

let f(x) = −2x² + 28x + 20  

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

f(x) = −2(x² - 14x) + 20  

f(x) = −2(x² - 14x +49) - {-2(49) + 20}

f(x) = −2(x² - 14x +49) + 98 + 20

f(x) = −2(x² - 7)² + 118  

The equivalent expression that reveals the video game price that produces the highest weekly profit is -2(x-7)^2+118 and the price is $7