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