Problem preview

F-IF.6 Warmup M2-020-A07-V04

Calculate, estimate, and interpret average rate of change for quadratic functions.

Calculate and compare average rates of change of a quadratic over intervals

Problem

For \(p(x)=-(x-5)^{2}+16\), find and compare the average rates on \([1,3]\) and \([3,5]\). Show endpoint values and quotients, identify the larger rate and difference, and explain why growth slows near the maximum.

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Rates: (12−0)/(3−1)=6 and (16−12)/(5−3)=6; the rates are equal.

Rates: (12−0)/(3−1)=6 and (16−12)/(5−3)=2; the first rate is larger by 4.

Rates: (12−0)/(3−1)=6 and (16−0)/(5−1)=4; the first rate is larger by 2.

Rates: 12−0=12 and 16−12=4; the first rate is larger by 8.

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Curriculum context

Course: Math II
Standard: F-IF.6
Category: Functions
Domain: Interpreting Functions
Objective: Calculate, estimate, and interpret average rate of change for quadratic functions.
Problem type: Calculate and compare average rates of change of a quadratic over intervals