Find the $y$-intercept of $P(x)=-x^{2}+10x-24$ when $x$ is whole-number items sold and $P$ is profit in dollars. Evaluate $P(0)$, state the signed intercept, and translate the negative profit into a loss statement.

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At x=0 items sold, P(0)=−$24, so the model represents a $24 loss at zero sales.

At x=0 items sold, P(0)=$24, so the model represents a $24 profit at zero sales.

At x=0 items sold, P(0)=−$1, so the model represents a $1 loss at zero sales.

At x=24 items sold, P(24)=$0, so the y-intercept occurs at 24 items.

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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 y-intercept of a quadratic model in context