Interpret the axis $q=8$ for $P(q)=-(q-8)^{2}+49$ when $q$ is a whole-number item quantity. State the maximum profit, explain equal profit for admissible quantities equally far from $8$, and verify $\text{one}$ symmetric whole-number pair.

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The symmetry rule pairs q=7.5 with q=8.5 in the whole-number domain.

The axis is q=8 items; maximum profit is $49 there, and whole-number quantities equally far from 8 have equal modeled profit.

The symmetry rule is P(8−d)=P(8+2d).

The axis is profit $49, and the maximum quantity is 8 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 axis of symmetry of a quadratic model in context