Domanda del libro di testo
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| b. f(-5)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 39
Write the standard form of the equation of the circle with the given center and radius. Center (-4, 0), r = 10
Guida verificata passo dopo passo1
Recall the standard form of the equation of a circle is given by: \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.
Identify the center \( (h, k) \) from the problem: here, the center is \( (-4, 0) \), so \( h = -4 \) and \( k = 0 \).
Substitute the values of \( h \) and \( k \) into the standard form: \( (x - (-4))^2 + (y - 0)^2 = r^2 \).
Simplify the expression inside the parentheses: \( (x + 4)^2 + y^2 = r^2 \).
Substitute the radius \( r = 10 \) and square it to get \( r^2 = 10^2 = 100 \), so the equation becomes \( (x + 4)^2 + y^2 = 100 \).
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Standard Form of a Circle's Equation
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 directly relates the coordinates of any point on the circle to its center and radius.
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5:18
Circles in Standard Form
Coordinates of the Center
The center of the circle is given as a point (h, k). In the equation, these values are used as (x - h) and (y - k) to measure the horizontal and vertical distances from the center to any point on the circle.
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05:10Graphs & the Rectangular Coordinate System
Radius and Squaring
The radius r is the distance from the center to any point on the circle. In the equation, the radius is squared (r²) to relate it to the sum of the squared distances along the x and y axes, ensuring all points satisfy the circle's definition.
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06:24Solving Quadratic Equations by Completing the Square
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