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F-BF.3 Warmup M2-016-A06-V02

Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.

Write a quadratic function from a vertex and one other graph feature

Problem

Construct the quadratic shown by the feature plot: vertex \((-1,4)\), downward opening, and point \((0,1)\). Write \(f(x)=a(x+1)^{2}+4\), use the point to determine \(a\), and verify the resulting function's vertex, opening, and point.

Quadratic feature-givens plot marking vertex (−1, 4) and point (0, 1), with a downward-opening cue; no completed curve or equation is shown. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
F-BF.3
Category
Functions
Domain
Building Functions
Objective
Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Problem type
Write a quadratic function from a vertex and one other graph feature