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