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

Respuesta :

Answer:

[tex]-2(x-6)^2+246[/tex], x = $6

Step-by-step explanation:

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

Let [tex]f(x)=-2x^2+24x+174[/tex]

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

[tex]f(x)=-2(x^2-12x)+174[/tex]

[tex]f(x)=-2(x^2-12x+36)--2(36)+174[/tex]

[tex]f(x)=-2(x^2-12x+36)+72+174[/tex]

[tex]f(x)=-2(x-6)^2+246[/tex]

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

and the price is $6

Answer:

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

Hope it helps!

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