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F-IF.9 Warmup M2-025-A04-V04

Compare function properties across representations, especially quadratic comparisons.

Compare two quadratic axes of symmetry

Problem

Compare these axes of symmetry: \(A(x)=-(x+4)(x-2)\); \(B(x)=x^{2}+2x-3\).

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A method=uses one zero -4 as axis; A axis=x=-4; B method=x=−b/(2a)=−2/2=-1; B axis=x=-1; relation=A axis left of B; horizontal separation=3

A method=midpoint of zeros(-4+2)/2=-1; A axis=x=-1; B method=x=−b/(2a)=−2/2=-1; B axis=x=-1; relation=same axis; horizontal separation=0

A method=sign-error midpoint(-4−2)/2=-3; A axis=x=-3; B method=x=−b/(2a)=−2/2=-1; B axis=x=-1; relation=A axis left of B; horizontal separation=2

A method=midpoint of zeros(-4+2)/2=-1; A axis=x=-1; B method=x=b/(2a)=2/2=1; B axis=x=1; relation=A axis left of B; horizontal separation=2

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Curriculum context

Course: Math II
Standard: F-IF.9
Category: Functions
Domain: Interpreting Functions
Objective: Compare function properties across representations, especially quadratic comparisons.
Problem type: Compare two quadratic axes of symmetry