For $R(p)=-(p-12)^{2}+144$, where $p$ is price in dollars and $R$ is revenue in dollars, interpret the vertex. Identify both coordinates with units, determine the extremum from the opening, check the nonnegative-price context, and state the business conclusion.

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The model predicts maximum revenue of $144 at a price of $0.

The model predicts maximum revenue of $144 at a price of $12.

The model predicts maximum revenue of $12 at a price of $144.

The model predicts minimum revenue of $144 at a price of $12.

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Curriculum context

Course: Math II
Standard: F-IF.4
Category: Functions
Domain: Interpreting Functions
Objective: Interpret key graph/table features of quadratic models in context.
Problem type: Interpret the vertex of a quadratic model in context