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Mathematics

1 answer:

Lady_Fox [76]3 years ago

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Vitek1552 [10]

Answer:

$y=-2\,(x-6)^2+246$

with the video game cost of x = $6

This agrees with the last option in the list of possible answers

Step-by-step explanation:

Recall that the maximum of a parabola resides at its vertex. So let's find the x and y position of that vertex, by using first the fact that the x value of the vertex of a parabola of general form:

$y=ax^2+bx+c$

is given by:

$x_{vertex}=\frac{-b}{2\,a}$

In our case, the quadratic expression that generates the parabola is:

$y=-2x^2+24x+174$

then the x-position of its vertex is:

$x_{vertex}=\frac{-b}{2\,a}\\x_{vertex}=\frac{-24}{2\,(-2)}\\x_{vertex}=\frac{-24}{-4)}\\x_{vertex}=6$

This is the price of the video game that produces the maximum profit (x = $6). Now let's find the y-position of the vertex using the actual equation for this value of x:

$y=-2x^2+24x+174\\y_{vertex}=-2\,(6)^2+24\,(6)+174\\y_{vertex}=-72+144+174\\y_{vertex}=246$

This value is the highest weekly profit (y = $246).

Now, recall that we can write the equation of the parabola in what is called "vertex form" using the actual values of the vertex position $(x_{vertex},y_{vertex})$ :