Problem preview

F-IF.6 Warmup M2-020-A07-V03

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

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

Problem

Calculate the average rates of \(h(x)=x^{2}-4x\) on \([0,2]\) and \([2,4]\). Evaluate \(h\) at \(\text{all}~\text{endpoints}\), display each quotient, compare signed rates and magnitudes, and connect them to the vertex at \(x=2\).

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Rates: (−4−0)/(2−0)=−2 and (0−0)/(4−0)=0; the second rate is larger by 2.

Rates: (−4−0)/(2−0)=−2 and (0−(−4))/(4−2)=2; the signed rates are opposite and have equal magnitude.

Rates: (−4−0)/(2−0)=2 and (0−(−4))/(4−2)=2; the rates are equal.

Rates: −4−0=−4 and 0−(−4)=4; the signed rates are opposite with magnitude 4.

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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