Solving a Real-World Problem Using Quadratic Equations

8.2.4 Solving a Real-World Problem Using Quadratic Equations

8.2.4 • Solving a Real-World Problem Using Quadratic Equations

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A movie theater models the revenue from ticket sales in one day as a function of the ticket price, $p$ . Here are two expressions defining the same revenue function.

$p (120 - 4 p)$

$120 p - 4 p^{2}$

According to this model, how high would the ticket price have to be for the theater to make $0 in revenue? Be prepared to show your reasoning.

Compare your answer:

$30. If $p (120 - 4 p) = 0$ , then either $p = 0$ or $120 - 4 p = 0$ . If the latter is a true equation, $p$ must be 30.

What equation can you write to find out what ticket price(s) would allow the theater to make $600 in revenue?

Compare your answer:

$p (120 - 4 p) = 600$ or $120 p - 4 p^{2} = 600$