Beginning and Intermediate Algebra
5th Edition
ISBN: 9781259616754
Author: Julie Miller, Molly O'Neill, Nancy Hyde
Publisher: McGraw-Hill Education
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Chapter 13.1, Problem 84PE
To determine
To graph: The equation
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For Exercises 27–34, an equation of a parabola x = 4py or y = 4px is given.
a. Identify the vertex, value of p, focus, and focal diameter of the parabola.
b. Identify the endpoints of the latus rectum.
c. Graph the parabola.
d. Write equations for the directrix and axis of symmetry. (See Examples 2-3)
27. x
-4y
28. x
-20y
29. 10y
= 80x
30. 3y = 12x
31. 4x
40y
32. 2x
14y
33. y =
34. y = -2x
= -X
%3D
For Exercises 67–70, identify the equation as representing an ellipse or a hyperbola, and match the equation with the graph.
(x – 5)²
67.
(y + 2)²
= 1
(x – 5)?
68.
(y + 2)?
= 1
49
36
36
49
(x - 5)?
69.
(y + 2)²
= 1
(y + 2)²
= 1
(x - 5)?
49
36
70.
49
36
А.
В.
С.
D.
15
12
41
6
-6-4-2
4 6 8 10 12 14
4 6 8 10 12 14
-6 -4
2.
4 6 8 10l 12 14
-6
1k 15 18 21
-6
2.
Obtain the graph of the parabola y = -x² + 4x using transformations of
the graph of y = x². Explain each step.
Chapter 13 Solutions
Beginning and Intermediate Algebra
Ch. 13.1 - Find the distance between the points ( − 4 , − 2 )...Ch. 13.1 - Prob. 2SPCh. 13.1 - Prob. 3SPCh. 13.1 - Prob. 4SPCh. 13.1 - Prob. 5SPCh. 13.1 - Prob. 6SPCh. 13.1 - Prob. 7SPCh. 13.1 - Prob. 8SPCh. 13.1 - Prob. 1PECh. 13.1 - Prob. 2PE
Ch. 13.1 - Prob. 3PECh. 13.1 - Prob. 4PECh. 13.1 - Prob. 5PECh. 13.1 - Prob. 6PECh. 13.1 - Prob. 7PECh. 13.1 - Prob. 8PECh. 13.1 - Prob. 9PECh. 13.1 - Prob. 10PECh. 13.1 - Prob. 11PECh. 13.1 - Prob. 12PECh. 13.1 - Prob. 13PECh. 13.1 - Prob. 14PECh. 13.1 - Prob. 15PECh. 13.1 - Prob. 16PECh. 13.1 - Prob. 17PECh. 13.1 - Prob. 18PECh. 13.1 - Prob. 19PECh. 13.1 - Prob. 20PECh. 13.1 - Prob. 21PECh. 13.1 - Prob. 22PECh. 13.1 - Prob. 23PECh. 13.1 - Prob. 24PECh. 13.1 - Prob. 25PECh. 13.1 - Prob. 26PECh. 13.1 - Prob. 27PECh. 13.1 - Prob. 28PECh. 13.1 - Prob. 29PECh. 13.1 - Prob. 30PECh. 13.1 - Prob. 31PECh. 13.1 - Prob. 32PECh. 13.1 - Prob. 33PECh. 13.1 - Prob. 34PECh. 13.1 - Prob. 35PECh. 13.1 - Prob. 36PECh. 13.1 - Prob. 37PECh. 13.1 - Prob. 38PECh. 13.1 - Prob. 39PECh. 13.1 - Prob. 40PECh. 13.1 - Prob. 41PECh. 13.1 - Prob. 42PECh. 13.1 - Prob. 43PECh. 13.1 - Prob. 44PECh. 13.1 - Prob. 45PECh. 13.1 - Prob. 46PECh. 13.1 - Prob. 47PECh. 13.1 - Prob. 48PECh. 13.1 - For Exercises 49–54, write an equation that...Ch. 13.1 - Prob. 50PECh. 13.1 - Prob. 51PECh. 13.1 - Prob. 52PECh. 13.1 - Prob. 53PECh. 13.1 - Prob. 54PECh. 13.1 - Prob. 55PECh. 13.1 - Prob. 56PECh. 13.1 - Prob. 57PECh. 13.1 - Prob. 58PECh. 13.1 - Prob. 59PECh. 13.1 - Prob. 60PECh. 13.1 - Prob. 61PECh. 13.1 - Prob. 62PECh. 13.1 - Prob. 63PECh. 13.1 - Prob. 64PECh. 13.1 - Prob. 65PECh. 13.1 - Prob. 66PECh. 13.1 - Prob. 67PECh. 13.1 - Prob. 68PECh. 13.1 - Prob. 69PECh. 13.1 - For Exercises 65–72, find the midpoint of the line...Ch. 13.1 - For Exercise 65-72, find the midpoint of the line...Ch. 13.1 - For Exercise 65-72, find the midpoint of the line...Ch. 13.1 - Prob. 73PECh. 13.1 - Prob. 74PECh. 13.1 - For Exercises 75–78, the two given points are...Ch. 13.1 - Prob. 76PECh. 13.1 - Prob. 77PECh. 13.1 - Prob. 78PECh. 13.1 - Prob. 79PECh. 13.1 - Prob. 80PECh. 13.1 - Prob. 81PECh. 13.1 - Prob. 82PECh. 13.1 - Prob. 83PECh. 13.1 - Prob. 84PECh. 13.1 - Prob. 85PECh. 13.1 - Prob. 86PECh. 13.1 - Prob. 87PECh. 13.1 - Prob. 88PECh. 13.2 - Prob. 1SPCh. 13.2 - Prob. 2SPCh. 13.2 - Prob. 3SPCh. 13.2 - Prob. 4SPCh. 13.2 - Prob. 5SPCh. 13.2 - Prob. 6SPCh. 13.2 - Prob. 7SPCh. 13.2 - Prob. 8SPCh. 13.2 - Prob. 9SPCh. 13.2 - Prob. 10SPCh. 13.2 - Prob. 11SPCh. 13.2 - 1. a. A circle, a parabola, an ellipse, and a...Ch. 13.2 - Prob. 2PECh. 13.2 - Prob. 3PECh. 13.2 - Prob. 4PECh. 13.2 - Prob. 5PECh. 13.2 - Prob. 6PECh. 13.2 - Prob. 7PECh. 13.2 - Prob. 8PECh. 13.2 - Prob. 9PECh. 13.2 - Prob. 10PECh. 13.2 - Prob. 11PECh. 13.2 - Prob. 12PECh. 13.2 - Prob. 13PECh. 13.2 - Prob. 14PECh. 13.2 - Prob. 15PECh. 13.2 - Prob. 16PECh. 13.2 - Prob. 17PECh. 13.2 - Prob. 18PECh. 13.2 - Prob. 19PECh. 13.2 - Prob. 20PECh. 13.2 - Prob. 21PECh. 13.2 - Prob. 22PECh. 13.2 - Prob. 23PECh. 13.2 - Prob. 24PECh. 13.2 - Prob. 25PECh. 13.2 - For Exercises 25–33, determine the vertex by using...Ch. 13.2 - Prob. 27PECh. 13.2 - Prob. 28PECh. 13.2 - Prob. 29PECh. 13.2 - Prob. 30PECh. 13.2 - Prob. 31PECh. 13.2 - Prob. 32PECh. 13.2 - Prob. 33PECh. 13.2 - Prob. 34PECh. 13.2 - Prob. 35PECh. 13.2 - Prob. 36PECh. 13.2 - Prob. 37PECh. 13.2 - Prob. 38PECh. 13.2 - Prob. 39PECh. 13.2 - Prob. 40PECh. 13.2 - Prob. 41PECh. 13.2 - Prob. 42PECh. 13.2 - Prob. 43PECh. 13.2 - Prob. 44PECh. 13.2 - Prob. 45PECh. 13.2 - Prob. 46PECh. 13.2 - Prob. 47PECh. 13.2 - Prob. 48PECh. 13.2 - Prob. 49PECh. 13.3 - Prob. 1SPCh. 13.3 - Prob. 2SPCh. 13.3 - Prob. 3SPCh. 13.3 - Prob. 4SPCh. 13.3 - Prob. 5SPCh. 13.3 - Prob. 1PECh. 13.3 - Prob. 2PECh. 13.3 - Prob. 3PECh. 13.3 - Prob. 4PECh. 13.3 - Prob. 5PECh. 13.3 - Prob. 6PECh. 13.3 - Prob. 7PECh. 13.3 - Prob. 8PECh. 13.3 - Prob. 9PECh. 13.3 - Prob. 10PECh. 13.3 - Prob. 11PECh. 13.3 - Prob. 12PECh. 13.3 - Prob. 13PECh. 13.3 - Prob. 14PECh. 13.3 - Prob. 15PECh. 13.3 - Prob. 16PECh. 13.3 - Prob. 17PECh. 13.3 - Prob. 18PECh. 13.3 - Prob. 19PECh. 13.3 - Prob. 20PECh. 13.3 - Prob. 21PECh. 13.3 - Prob. 22PECh. 13.3 - Prob. 23PECh. 13.3 - Prob. 24PECh. 13.3 - Prob. 25PECh. 13.3 - Prob. 26PECh. 13.3 - Prob. 27PECh. 13.3 - Prob. 28PECh. 13.3 - Prob. 29PECh. 13.3 - Prob. 30PECh. 13.3 - Prob. 31PECh. 13.3 - Prob. 32PECh. 13.3 - Prob. 33PECh. 13.3 - Prob. 34PECh. 13.3 - Prob. 35PECh. 13.3 - Prob. 36PECh. 13.3 - Prob. 37PECh. 13.3 - Prob. 38PECh. 13.3 - For Exercises 33–40, use the equation in standard...Ch. 13.3 - Prob. 40PECh. 13.3 - Prob. 41PECh. 13.3 - Prob. 42PECh. 13.3 - Prob. 43PECh. 13.3 - Prob. 44PECh. 13.3 - Prob. 45PECh. 13.3 - Prob. 46PECh. 13.3 - Prob. 47PECh. 13.3 - Prob. 48PECh. 13.3 - Prob. 49PECh. 13.3 - Prob. 50PECh. 13.3 - Prob. 51PECh. 13.3 - Prob. 52PECh. 13.3 - Prob. 53PECh. 13.3 - Prob. 54PECh. 13.3 - Prob. 55PECh. 13.3 - Prob. 56PECh. 13.3 - Prob. 57PECh. 13.3 - Prob. 58PECh. 13.3 - Prob. 1PRECh. 13.3 - For Exercises 1–8, identify the formula. x 2 a 2 +...Ch. 13.3 - Prob. 3PRECh. 13.3 - Prob. 4PRECh. 13.3 - Prob. 5PRECh. 13.3 - Prob. 6PRECh. 13.3 - Prob. 7PRECh. 13.3 - Prob. 8PRECh. 13.3 - Prob. 9PRECh. 13.3 - Prob. 10PRECh. 13.3 - Prob. 11PRECh. 13.3 - Prob. 12PRECh. 13.3 - Prob. 13PRECh. 13.3 - Prob. 14PRECh. 13.3 - Prob. 15PRECh. 13.3 - Prob. 16PRECh. 13.3 - Prob. 17PRECh. 13.3 - Prob. 18PRECh. 13.3 - Prob. 19PRECh. 13.3 - Prob. 20PRECh. 13.3 - Prob. 21PRECh. 13.3 - Prob. 22PRECh. 13.3 - Prob. 23PRECh. 13.3 - Prob. 24PRECh. 13.3 - Prob. 25PRECh. 13.3 - Prob. 26PRECh. 13.3 - Prob. 27PRECh. 13.3 - Prob. 28PRECh. 13.3 - Prob. 29PRECh. 13.3 - Prob. 30PRECh. 13.4 - Given the system 2 x + y = 5 x 2 + y 2 = 50 Solve...Ch. 13.4 - Prob. 2SPCh. 13.4 - Prob. 3SPCh. 13.4 - Prob. 4SPCh. 13.4 - Solve the system by using the substitution method....Ch. 13.4 - Prob. 6SPCh. 13.4 - 1. a. A _______ system of equations in two...Ch. 13.4 - Prob. 2PECh. 13.4 - Prob. 3PECh. 13.4 - Prob. 4PECh. 13.4 - Prob. 5PECh. 13.4 - Prob. 6PECh. 13.4 - Prob. 7PECh. 13.4 - Prob. 8PECh. 13.4 - Prob. 9PECh. 13.4 - Prob. 10PECh. 13.4 - Prob. 11PECh. 13.4 - Prob. 12PECh. 13.4 - Prob. 13PECh. 13.4 - Prob. 14PECh. 13.4 - Prob. 15PECh. 13.4 - Prob. 16PECh. 13.4 - For Exercises 17–22, sketch each system of...Ch. 13.4 - Prob. 18PECh. 13.4 - Prob. 19PECh. 13.4 - Prob. 20PECh. 13.4 - Prob. 21PECh. 13.4 - Prob. 22PECh. 13.4 - Prob. 23PECh. 13.4 - Prob. 24PECh. 13.4 - Prob. 25PECh. 13.4 - Prob. 26PECh. 13.4 - Prob. 27PECh. 13.4 - Prob. 28PECh. 13.4 - Prob. 29PECh. 13.4 - Prob. 30PECh. 13.4 - Prob. 31PECh. 13.4 - Prob. 32PECh. 13.4 - Prob. 33PECh. 13.4 - Prob. 34PECh. 13.4 - Prob. 35PECh. 13.4 - Prob. 36PECh. 13.4 - Prob. 37PECh. 13.4 - For Exercises 32–48, solve the system of nonlinear...Ch. 13.4 - For Exercises 32–48, solve the system of nonlinear...Ch. 13.4 - Prob. 40PECh. 13.4 - Prob. 41PECh. 13.4 - Prob. 42PECh. 13.4 - Prob. 43PECh. 13.4 - Prob. 44PECh. 13.4 - Prob. 45PECh. 13.4 - Prob. 46PECh. 13.4 - Prob. 47PECh. 13.4 - For Exercises 32–48, solve the system of nonlinear...Ch. 13.4 - Prob. 49PECh. 13.4 - Prob. 50PECh. 13.4 - Prob. 51PECh. 13.4 - Prob. 52PECh. 13.4 - Prob. 53PECh. 13.4 - Prob. 54PECh. 13.4 - Prob. 55PECh. 13.4 - Prob. 56PECh. 13.4 - Prob. 57PECh. 13.4 - Prob. 58PECh. 13.5 - Graph the solution set of the inequality. x 2 + y...Ch. 13.5 - Prob. 2SPCh. 13.5 - Prob. 3SPCh. 13.5 - Prob. 4SPCh. 13.5 - Prob. 1PECh. 13.5 - Prob. 2PECh. 13.5 - Prob. 3PECh. 13.5 - Prob. 4PECh. 13.5 - Prob. 5PECh. 13.5 - Prob. 6PECh. 13.5 - Prob. 7PECh. 13.5 - Prob. 8PECh. 13.5 - For Exercises 1–12, match the equation with its...Ch. 13.5 - Prob. 10PECh. 13.5 - Prob. 11PECh. 13.5 - For Exercises 1–12, match the equation with its...Ch. 13.5 - Prob. 13PECh. 13.5 - Prob. 14PECh. 13.5 - Prob. 15PECh. 13.5 - Prob. 16PECh. 13.5 - a. Graph the solution set for x 2 + y 2 ≤ 9 . b....Ch. 13.5 - a. Graph the solution set for x 2 4 + y 2 9 ≥ 1....Ch. 13.5 - 19. a. Graph the solution set for.
b. How would...Ch. 13.5 - 20. a. Graph the solution set for
b. How...Ch. 13.5 - Prob. 21PECh. 13.5 - 22. A coordinate system is placed at the center of...Ch. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - Prob. 25PECh. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - Prob. 27PECh. 13.5 - Prob. 28PECh. 13.5 - Prob. 29PECh. 13.5 - Prob. 30PECh. 13.5 - Prob. 31PECh. 13.5 - Prob. 32PECh. 13.5 - Prob. 33PECh. 13.5 - Prob. 34PECh. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - For Exercises 23–37, graph the solution set. (See...Ch. 13.5 - Prob. 37PECh. 13.5 - For Exercises 38–51, graph the solution set to the...Ch. 13.5 - Prob. 39PECh. 13.5 - Prob. 40PECh. 13.5 - Prob. 41PECh. 13.5 - Prob. 42PECh. 13.5 - Prob. 43PECh. 13.5 - Prob. 44PECh. 13.5 - Prob. 45PECh. 13.5 - Prob. 46PECh. 13.5 - Prob. 47PECh. 13.5 - Prob. 48PECh. 13.5 - Prob. 49PECh. 13.5 - Prob. 50PECh. 13.5 - Prob. 51PECh. 13.5 - Prob. 52PECh. 13.5 - Prob. 53PECh. 13.5 - Prob. 54PECh. 13.5 - Prob. 55PECh. 13 - For Exercises 1-2, find the distance between the...Ch. 13 - For Exercises 1-2, find the distance between the...Ch. 13 - Find x such that ( x , 5 ) is 5 units from ( 2 , 9...Ch. 13 - 4. Find x such that is 3 units from
Ch. 13 - Prob. 5RECh. 13 - For Exercises 5–8, find the center and the radius...Ch. 13 - Prob. 7RECh. 13 - For Exercises 5–8, find the center and the radius...Ch. 13 - Prob. 9RECh. 13 - For Exercises 10–13, write the equation of the...Ch. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - For Exercises 16–17, find the midpoint of the...Ch. 13 - For Exercises 16–17, find the midpoint of the...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 18–21, determine whether the axis of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 22–25, determine the coordinates of...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 26–29, write the equation in...Ch. 13 - For Exercises 30–31, identify the x- and...Ch. 13 - For Exercises 30–31, identify the x- and...Ch. 13 - For Exercises 32–33, identify the center of the...Ch. 13 - For Exercises 32–33, identify the center of the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 34–37, determine whether the...Ch. 13 - For Exercises 38–39, graph the hyperbola by first...Ch. 13 - For Exercises 38–39, graph the hyperbola by first...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 40–43, identify the equations as...Ch. 13 - For Exercises 44–47, a. Identify each equation as...Ch. 13 - For Exercises 44–47,
a. Identify each equation as...Ch. 13 - For Exercises 44–47, a. Identify each equation as...Ch. 13 - For Exercises 44–47,
a. Identify each equation as...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 48–53, solve the system of nonlinear...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 54–59, graph the solution set to the...Ch. 13 - For Exercises 60–61, graph the solution set to the...Ch. 13 - For Exercises 60–61, graph the solution set to the...Ch. 13 - 1. Use the distance formula to find the distance...Ch. 13 - Prob. 2TCh. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - 5. Find the center of the circle that has a...Ch. 13 - Determine the vertex and the equation of the axis...Ch. 13 - Write the equation in standard form y = a ( x − h...Ch. 13 - 8. Graph the ellipse.
Ch. 13 - 9. Graph the ellipse.
Ch. 13 - Graph the hyperbola. y 2 − x 2 4 = 1Ch. 13 - For Exercises 11–12, solve the system and identify...Ch. 13 - For Exercises 11–12, solve the system and identify...Ch. 13 - Describe the circumstances in which a nonlinear...Ch. 13 - 14. Solve the system by using either the...Ch. 13 - For Exercises 15–18, graph the solution...Ch. 13 - For Exercises 15–18, graph the solution...Ch. 13 - For Exercises 15–18, graph the solution set. x < y...Ch. 13 - For Exercises 15–18, graph the solution set. y < x...Ch. 13 - Solve. 5 ( 2 y − 1 ) = 2 y − 4 + 8 y − 1Ch. 13 - Solve the inequality. Graph the solution and write...Ch. 13 - The product of two integers is 150. If one integer...Ch. 13 - For 5 y − 3 x − 15 = 0 , a. Find the x- and...Ch. 13 - Find the slope and y-intercept of 3 x − 4 y = 6.Ch. 13 - 6. A collection of dimes and quarters has a total...Ch. 13 - Solve the system. x + y = −...Ch. 13 - 8. Solve the system.
Ch. 13 - Solve by using the Gauss-Jordan method. 3 x − 4 y...Ch. 13 - 10. For find the function values and.
Ch. 13 - 11. Solve the inequality.
Ch. 13 - 12. The quantity z varies jointly as y and as the...Ch. 13 - 13. For find
Ch. 13 - a. Find the value of the expression x 3 + x 2 + x...Ch. 13 - Factor completely. x 2 − y 2 − 6 x − 6 yCh. 13 - 16. Multiply.
Ch. 13 - Solve. 2 x ( x − 7 ) = x − 18Ch. 13 - Simplify. 3 a 2 − a − 2 3 a 2 + 8 a + 4Ch. 13 - Subtract. 2 x + 3 − x x − 2Ch. 13 - 20. Solve.
Ch. 13 - Prob. 21CRECh. 13 - For Exercises 22–23, perform the indicated...Ch. 13 - For Exercises 22–23, perform the indicated...Ch. 13 - Find the length of the missing side.Ch. 13 - An automobile starts from rest and accelerates at...Ch. 13 - Solve the equation 125 w 2 + 1 = 0 by factoring...Ch. 13 - 27. Solve.
Ch. 13 - 28. Find the coordinates of the vertex of the...Ch. 13 - Graph the quadratic function defined by g ( x ) =...Ch. 13 - 30. Solve the inequality and write the answer in...Ch. 13 - Solve the inequality. | 2 x − 5 | ≥ 4Ch. 13 - Write the expression in logarithmic form. 8 5 / 3...Ch. 13 - Solve. 5 2 = 125 xCh. 13 - 34. For
Ch. 13 - Prob. 35CRECh. 13 - 36. Graph the ellipse.
Ch. 13 - 37. Determine the center of the circle, given the...Ch. 13 - 38. Solve the system of nonlinear equations.
Ch. 13 - 39. Graph the solution set.
Ch. 13 - Graph the solution set to this system. y > ( 1 2 )...
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