Problem preview

F-IF.7.a Warmup M1-025-A11-V03

Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.

Sketch a quadratic from key features

Problem

Derive the simplest upward-opening quadratic with vertex \((-3,~4)\) and \(a~=~1\), and graph it on the grid. State the equation, axis of symmetry, a symmetric point pair, real-zero verdict, \(y\)-intercept, and range.

Blank coordinate grid tailored to plotting y=(x+3)²+4 without any completed curve or feature labels.

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equation = y=(x-3)²+4; vertex (3,4)

equation = y=(x+3)²+4; vertex = (-3,4); axis = x=-3; symmetric pair = (-4,5),(-2,5); real zeros = none because minimum 4>0; y-intercept = (0,13); range = [4,∞)

equation = y=(x+3)²-4; vertex (-3,-4); zeros -5,-1

equation = y=-(x+3)²+4; opens down; zeros -5,-1

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Curriculum context

Course: Math I
Standard: F-IF.7.a
Category: Functions
Domain: Interpreting Functions
Objective: Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Problem type: Sketch a quadratic from key features