question 5(multiple choice worth 1 points) (08.02 mc) the owner of a video - game store creates the…

question 5(multiple choice worth 1 points) (08.02 mc) the owner of a video - game store creates the expression - 2x^{2}+32x - 8 to represent the stores 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^{2}-16x)-8;x = $16 - 2(x^{2}-16x + 4);x = $4 - 2(x - 8)^{2}+120;x = $8 - 2(x - 8)^{2}+120;x = $120

question 5(multiple choice worth 1 points) (08.02 mc) the owner of a video - game store creates the expression - 2x^{2}+32x - 8 to represent the stores 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^{2}-16x)-8;x = $16 - 2(x^{2}-16x + 4);x = $4 - 2(x - 8)^{2}+120;x = $8 - 2(x - 8)^{2}+120;x = $120

Answer

Explanation:

Step1: Complete the square for $-2x^{2}+32x - 8$.

Factor out - 2 from the first two terms: $y=-2(x^{2}-16x)-8$. Take half of the coefficient of $x$ inside the parentheses, square it and add and subtract it inside the parentheses. The coefficient of $x$ is - 16, half of it is - 8, and $(-8)^{2}=64$. So $y=-2(x^{2}-16x + 64-64)-8$.

Step2: Rewrite the expression.

$y=-2((x - 8)^{2}-64)-8=-2(x - 8)^{2}+128 - 8=-2(x - 8)^{2}+120$. For a quadratic function in vertex - form $y=a(x - h)^{2}+k$ ($a\neq0$), if $a\lt0$, the vertex $(h,k)$ is the maximum point of the parabola. Here $a=-2\lt0$, and the vertex is $(8,120)$. The value of $x$ that maximizes the function is $x = 8$.

Answer:

C. $-2(x - 8)^{2}+120;x = $8$