Problem preview

F-IF.6 Warmup M2-020-A07-V02

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

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

Problem

Compute the average rates of \(g(x)=-(x-3)^{2}+9\) on \([0,3]\) and \([3,6]\). Show the endpoint evaluations and quotients, compare signs and magnitudes, and explain the result using symmetry about \(x=3\).

Answer choices

Choose your path.

Preview only

Rates: (9−0)/(3−0)=3 and (0−0)/(6−0)=0; the first rate is larger by 3.

Rates: (9−0)/(3−0)=3 and (0−9)/(6−3)=3; the rates are equal.

Rates: (9−0)/(3−0)=3 and (0−9)/(6−3)=−3; the signed rates are opposite and have equal magnitude.

Rates: 9−0=9 and 0−9=−9; the signed rates are opposite with magnitude 9.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

More than a preview

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

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