Problem preview

F-IF.8.a Warmup M2-023-A09-V03

Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.

Complete the square and identify the extremum

Problem

Complete the square for \(2x^{2}+8x+1\) by factoring \(2\) from the quadratic and linear terms, then completing \(x^{2}+4x\) with \(4\). Write the equivalent vertex form, expand it as a check, and state the vertex and extremum type.

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2(x+2)²−7; vertex (−2,−7), minimum.

2(x+4)²−31; vertex (−4,−31), minimum.

2(x+2)²+1; vertex (−2,1), minimum.

2(x+2)²−7; vertex (2,−7), minimum.

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Curriculum context

Course: Math II
Standard: F-IF.8.a
Category: Functions
Domain: Interpreting Functions
Objective: Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Problem type: Complete the square and identify the extremum