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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. −2(x − 7)2 118; x = $7 −2(x − 7)2 118; x = $118 −2(x2 − 14x) 20; x = $14 −2(x2 − 14x − 10); x = $10

Sagot :

The given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex]price is $7 option first is correct.

What is a quadratic expression?

A quadratic expression is a second-degree algebraic expression represented by the:

[tex]\rm ax^2+bx+c=0[/tex] ........(1)

Where a, b, and c are the constants and  

We have a quadratic expression:

[tex]\rm f(x)=-2x^2+28x+20[/tex]

Convert it to perfect square by perfect square trinomial:

[tex]\rm f(x)=-2(x^2+14x)+20[/tex]  

[tex]\rm f(x)=-2(x^2+14x+49-49)+20[/tex]   (adding and subtracting by 49)

[tex]\rm f(x)=-2(x-7)^2+2(49)+20[/tex]

[tex]\rm f(x)=-2(x-7)^2+118[/tex]

Here [tex]\rm (x-7)^2[/tex] is the positive term and -2 is the negative term so in order to get the highest weekly profit it should be zero, so

[tex]\rm -2(x-7)^2=0[/tex]

x = $7

Thus, the given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex]  and the price is $7.

Learn more about quadratic expression here:

brainly.com/question/2263981

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