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F-IF.7.a Warmup M2-021-A09-V02

Graph linear and quadratic functions and identify intercepts, maxima, and minima.

Construct and validate a quadratic graph from key features

Problem

Construct a quadratic with vertex \((2,7)\), opening downward, and \(y\)-intercept \((0,3)\). Start with \(y=a(x-2)^{2}+7\), use the \(y\)-intercept to solve for \(a\), then verify the supplied point and opening direction against the graph scaffold. Identify the construction that passes every check.

A numeric coordinate grid marking only the supplied vertex (2, 7), y-intercept (0, 3), coordinate guides, and downward-opening cue. No completed curve or solved coefficient is shown. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
F-IF.7.a
Category
Functions
Domain
Interpreting Functions
Objective
Graph linear and quadratic functions and identify intercepts, maxima, and minima.
Problem type
Construct and validate a quadratic graph from key features