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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. R - Algebra ReviewProblem 49
Chapter 1, Problem 49

Concept Check Match each equation in Column I with its graph in Column II. I II 47. A. 48. B. 49. (x + 3)² + (y - 2)² = 25 C. 50. D.

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Identify the type of each equation in Column I. For example, recognize that an equation like \((x + 3)^2 + (y - 2)^2 = 25\) represents a circle with center at \((-3, 2)\) and radius \(5\) (since \(25\) is \$5^2$).
Recall the general forms of common graphs: circles, parabolas, ellipses, and hyperbolas, and their key features such as center, vertices, axes, and intercepts.
Analyze each graph in Column II by noting its shape and key points, such as the center of a circle or the vertex of a parabola, and compare these features to the equations in Column I.
Match each equation to the graph that corresponds to its shape and key characteristics. For example, the circle equation should match the graph showing a circle centered at \((-3, 2)\) with radius \(5\).
Double-check your matches by verifying that the graph's features (like intercepts or symmetry) align with the properties derived from the equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equation of a Circle

The equation (x + 3)² + (y - 2)² = 25 represents a circle centered at (-3, 2) with a radius of 5. Understanding this standard form helps identify the graph as a circle and locate its center and size.
Recommended video:
06:03
Equations of Circles & Ellipses

Graph Matching Techniques

Matching equations to graphs requires recognizing key features such as shape, intercepts, and transformations. This skill involves analyzing the equation's form and comparing it to visual characteristics of the graphs.
Recommended video:
4:08
Graphing Intercepts

Coordinate Geometry and Transformations

Understanding how shifts in x and y (like +3 or -2 inside the equation) translate the graph horizontally or vertically is essential. This concept helps in predicting the graph's position relative to the origin.
Recommended video:
5:25
Introduction to Transformations
Related Practice
Textbook Question

Find each product or quotient where possible. See Example 2. 100 / -25

Textbook Question

Add or subtract, as indicated. See Example 4. (3/2k) + (5/3k)

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Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. ƒ(x) = -x³ + 2x

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Textbook Question

For what value(s) of x is |x| = 4 true?

Textbook Question

Concept Check Match each equation in Column I with its graph in Column II. I II 47. (x - 3)² + (y - 2)² = 25 A. 48. B. 49. C. 50. D.

Textbook Question

Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(⅓)