Problem preview

G-GPE.3.1 Warmup M3-038-A10-V03

Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.

Classify a conic and fill only its defined measurements

Problem

Classify \((y~-~2)^2~=~12(x~+~4)\) and report the measurements defined for that conic: its vertex, \(p\)-value, and opening direction.

Answer choices

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It is a hyperbola; its center is (-4, 2); its semiaxes are a = 2sqrt(3) and b = 1; and it opens left and right.

It is an ellipse; its center is (-4, 2); its semiaxes are a = 2sqrt(3) and b = 1; and its major axis is horizontal.

It is a parabola; its vertex is (-4, 2); its focal parameter is p = 3; and it opens right.

It is a parabola; its vertex is (4, -2); its focal parameter is p = 12; and it opens left.

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Curriculum context

Course: Math III
Standard: G-GPE.3.1
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.
Problem type: Classify a conic and fill only its defined measurements