Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
3. Functions
Intro to Functions & Their Graphs
5:49 minutes
Problem 111
Textbook Question
Textbook QuestionIn Exercises 109–111, give the center and radius of each circle. x^2 + y^2 - 4x + 2y - 4 = 0
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Form of a Circle
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. This form allows for easy identification of the circle's center and radius by comparing it to the general equation of a circle.
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Circles in Standard Form
Completing the Square
Completing the square is a method used to transform a quadratic equation into a perfect square trinomial. This technique is essential for rewriting the given circle equation in standard form, enabling the identification of the center and radius.
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Solving Quadratic Equations by Completing the Square
Quadratic Terms in Circle Equations
In circle equations, the quadratic terms x² and y² represent the dimensions of the circle in the Cartesian plane. Understanding how these terms interact with linear terms (like -4x and +2y) is crucial for manipulating the equation to find the circle's center and radius.
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Circles in General Form
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