Math III · G-GPE.3.1

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

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

Concept Geometry
Domain Expressing Geometric Properties with Equations
Problem Types

Problem Templates In This Objective

13 problem types are attached to this objective. The full web app handles practice, answers, hints, and walkthroughs.

Template 1

Identify the type of conic by inspecting squared terms and signs in the equation

4 variants
Template 2

Complete squares and report every circle parameter

4 variants
Template 3

Complete squares and extract ellipse axes

4 variants
Template 4

Complete squares and extract hyperbola orientation

4 variants
Template 5

Complete a parabola and recover focus/directrix data

4 variants
Template 6

Read a circle's center, radius, and extents

4 variants
Template 7

Read every key feature of a standard ellipse

4 variants
Template 8

Read hyperbola center, vertices, and both asymptotes

4 variants
Template 9

Read complete parabola features from standard or vertex form

4 variants
Template 10

Classify a conic and fill only its defined measurements

4 variants
Template 11

Decide whether a conic equation is normal, degenerate, or has no real graph by inspecting squared terms and signs

4 variants
Template 12

Identify the graph features of a conic from its standard-form equation

4 variants
Template 13

Write a standard-form conic equation from graph features

4 variants