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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.

A)−2(x2 − 16x) − 8; x = $16
B)−2(x2 − 16x + 4); x = $4
C)−2(x − 8)2 + 120; x = $8
D)−2(x − 8)2 + 120; x = $120

Respuesta :

indrawboy

The equivalent expression that reveals the video game price that produces the highest weekly profit : C. -2(x-8)²+120; x = $8

Further explanation

The main composition of algebraic expressions are:

• 1. phrases / terms

• 2. variable

• 3. constants

• 4. arithmetic operations

• 5. coefficients

• 6. exponent

"Equivalent to" means having the same value

So the available answer choices have the same expression as the equation −2x² + 32x − 8

Let see the answer choices

A. -2(x²-16x)-8

[tex]\displaystyle -2x^2+ 32x-8 \Rightarrow equivalent\\\\x=16\\\\=-2.16^2+32.16-8\\\\=-512+512-8\\\\=-8[/tex]

B. -2(x²-16x+4)

[tex]\displaystyle -2x^2+32x-8 \Rightarrow equivalent\\\\x=4\\\\=-2.4^2+32.4-8\\\\=-32+128-8\\\\=88[/tex]

C. -2(x-8)²+120

[tex]\displaystyle -2(x^2-16x+64)+120\\\\=-2x^2+32x-128+120\\\\=-2x^2+32x-8 \Rightarrow equivalent\\\\x=8\\\\=-2.8^2+32.8-8\\\\=-128+256-8\\\\=120[/tex]

D. -2(x-8)²+120

[tex]\displaystyle -2(x^2-16x+64)+120\\\\=-2x^2+32x-128+120\\\\=-2x^2+32x-8 \Rightarrow equivalent\\\\x=120\\\\=-2.120^2+32.120-8\\\\=-28800+3840-8\\\\=-24968[/tex]

Learn more

The numerical coefficient

https://brainly.com/question/11050477

Keywords : video game store, the expression,weekly profit,price.

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qwerty1128

Answer:  C. -2(x-8)²+120; x = $8

Step-by-step explanation:

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