The owner of a video game store creates the expression −2x2 + 32x − 8 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.

To find the equivalent expression that reveals the video game price that produces the highest weekly profit, we need to complete the square for the given expression −2x2 + 32x − 8.

Starting with the expression -2x^2 + 32x - 8, we can factor out the -2 from the x^2 and x terms:
-2(x^2 - 16x) - 8

Now, to complete the square, we need to add and subtract (16/2)^2 = 64 to the expression inside the parentheses:
-2(x^2 - 16x + 64 - 64) - 8
-2((x - 8)^2 - 64) - 8
-2(x - 8)^2 + 128 - 8
-2(x - 8)^2 + 120

Therefore, the equivalent expression is −2(x − 8)2 + 120, and the price of the video game that produces the highest weekly profit is $8.