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The function p(x) = - 2(x-9)2 + 100 is used to determines the profit on T-shirts sold for x dollars. What would the profit from sales be if the proce of the T-shirts were $15 a piece?

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ANSWER

$28

EXPLANATION

The profit function is given as:

[tex]p(x) = - 2 {(x - 9)}^{2} + 100[/tex]

where x is the price of the T-shirt in dollars.

To find the profit on a T-shirt whose price is $15, we substitute x=15 into the function and simplify.

[tex]p(15) = - 2 {(15 - 9)}^{2} + 100[/tex]

We simplify to get:

[tex]p(15) = - 2 {(6)}^{2} + 100[/tex]

[tex]p(15) = -72+ 100[/tex]

[tex]p(15) = 28[/tex]