Problem preview

F-IF.7.a Warmup M1-025-A11-V02

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 downward-opening quadratic with zeros \(-1\) and \(5\) and leading coefficient \(a~=~-1\), and graph it on the grid. State the equation, zero behavior, axis of symmetry, vertex, \(y\)-intercept, and range.

Blank coordinate grid tailored to plotting y=−(x+1)(x−5) without any completed curve or feature labels.

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equation = y=(x+1)(x-5); opens up; vertex (2,-9)

equation = y=-(x+1)(x-5); axis x=-2; vertex (-2,9)

equation = y=-(x-1)(x+5); zeros 1,-5

equation = y=-(x+1)(x-5); zeros = -1,5, both simple and crossed; axis = x=2; vertex check = y(2)=-(3)(-3)=9, so (2,9); y-intercept = (0,5); range = (-∞,9]

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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