Problem preview
F-IF.5 Warmup M2-019-A06-V01

Relate the domain of a quadratic function to its graph and situation.

Determine the range of a quadratic function on a given interval domain

Problem

Given domain \(0~\le~x~\le~5\), determine the range of quadratic model \(f(x)=-(x-2)^2+9\).

Big Picture

What this problem is really about

A quadratic’s range on a closed interval comes from outputs actually attained on that interval, not from the full parabola. We’ll test both domain endpoints and any vertex inside the interval, compare those candidate outputs, and use continuity and endpoint inclusion to finish the range notation.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
F-IF.5
Category
Functions
Domain
Interpreting Functions
Objective
Relate the domain of a quadratic function to its graph and situation.
Problem type
Determine the range of a quadratic function on a given interval domain