Algebra II B Review 3 Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the equation. Describe the graph and its lines of symmetry. 1. a. c. b. graph is a circle of radius 5. Its center is at the origin. y-axis and the x-axis are lines of symmetry. d. graph is a circle of radius 25. Its center is at the origin. y-axis and the x-axis are lines of symmetry. graph is a circle of radius 25. Its center is at the origin. Every line through the center is a line of symmetry. graph is a circle of radius 5. Its center is at the origin. Every line through the center is a line of symmetry. 2.
a. c. b. graph is a circle. center is at the origin. Every line through the origin is a line of symmetry. d. graph is an ellipse. center is at the origin. It has two lines of symmetry, the x-axis and the y-axis. graph is an ellipse. center is at the origin. It has two lines of symmetry, the x-axis and the y-axis. graph is a circle. center is at the origin. Every line through the origin is a line of symmetry. 3.
b. graph is a hyperbola that consists of two branches. Its center is at the origin. It has two lines of symmetry, the x-axis and the y-axis. d. graph is a circle with radius 9. Its center is at the origin. Every line through the center is a line of symmetry. graph is a hyperbola that consists of two branches. Its center is at the origin. It has four lines of symmetry, the x-axis, the y-axis, y = x, and y = x. graph is a hyperbola that consists of two branches. Its center is at the origin. It has four lines of symmetry, the x-axis, the y-axis, y = x, and y = x. 4. Graph. Find the domain and range. a. c. domain is all real numbers. range is. domain is range is..
b. d. domain is range is all real numbers.. domain is is.. range Identify the center and intercepts of the conic section. n find the domain and range. 5. a. center of the ellipse is (0, 0). x-intercepts are ( 5, 0) and (5, 0). y-intercepts are (0, 9) and (0, 9). domain is {x 9 y 9}. range is {y 5 x 5}. b. center of the ellipse is (0, 0). x-intercepts are (0, 9) and (0, 9). y-intercepts are ( 5, 0) and (5, 0). domain is {x 5 x 5}. range is {y 9 y 9}. c. center of the ellipse is (0, 0). x-intercepts are ( 5, 0) and (5, 0). y-intercepts are (0, 9) and (0, 9). domain is {x 5 x 5}. range is {y 9 y 9}. d. center of the ellipse is (0, 0). x-intercepts are (0, 9) and (0, 9). y-intercepts are ( 5, 0) and (5, 0). domain is {x 9 y 9}. range is {y 5 x 5}.
6. a. center of the hyperbola is (0, 0). y-intercepts are (0, 2) and (0, 2). domain is all real numbers. range is {y y 2 or y 2}. b. center of the hyperbola is (0, 0). y-intercepts are (0, 2) and (0, 2). domain is all real numbers. range is {y y 2 or y 2}. c. center of the hyperbola is (0, 0). x-intercepts are (0, 2) and (0, 2). domain is all real numbers. range is {x x 2 or x 2}. d. center of the hyperbola is (0, 0). x-intercepts are (0, 2) and (0, 2). domain is all real numbers. range is {y y 2 or y 2}. 7. a. center of the circle is (0, 0). x-intercepts are (9, 0) and ( 9, 0). y-intercepts are (0, 9) and (0, 9). domain is {x 9 x 9}. range is {y 9 y 9}. b. center of the circle is (0, 0). x-intercepts are (9, 0) and ( 9, 0). y-intercepts are (0, 9) and (0, 9). domain is {y 9 y 9}. range is {x 9 x 9}. c. center of the circle is (9, 9). x-intercepts are (9, 0) and ( 9, 0). y-intercepts are (0, 9) and (0, 9). domain is {y 9 y 9}. range is {x 9 x 9}. d. center of the circle is (9, 9). x-intercepts are (9, 0) and ( 9, 0). y-intercepts are (0, 9) and (0, 9). domain is {x 9 x 9}. range is {y 9 y 9}. 8. This ellipse is being used for a design on a poster. Name the x-intercepts and y-intercepts of the graph.
9. Write an equation of a parabola with a vertex at the origin and a focus at ( 7, 0). 10. A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. pipe is located 7 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward. 11. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5. 12. Use the graph to write an equation for the parabola.
13. Which is the equation of the parabola that has a vertex at the origin and a focus at (3, 0)? 14. Graph.
15. Write an equation of a circle with center ( 7, 4) and radius 7. 16. Write an equation for the translation of, 7 units left and 5 units up. 17. Write an equation in standard form for the circle. 18. A satellite is launched in a circular orbit around Earth at an altitude of 100 miles above the surface. diameter of Earth is 7920 miles. Write an equation for the orbit of the satellite if the center of the orbit is the center of the Earth labeled (0, 0).
19. Find the center and radius of the circle with equation. a. (1, 5); 8 c. (1, 5); 64 b. ( 1, 5); 8 d. ( 1, 5); 64 20. Graph. 21. Write an equation in standard form of an ellipse that has a vertex at (3, 0), a co-vertex at (0, 5), and is centered at the origin. 22. An elliptical track has a major axis that is 80 yards long and a minor axis that is 74 yards long. Find an equation for the track if its center is (0, 0) and the major axis is the x-axis.
Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics. 23. vertices at ( 5, 0) and (0, 4) 24. height of 12 units and width of 19 units 25. height of 4 units and width of 5 units 26. Write an equation for the graph. 27. Graph the conic section.
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Algebra II B Review 3 Answer Section MULTIPLE CHOICE 1. ANS: D OBJ: 10-1.1 Graphing Equations of Conic Sections STA: MI G1.7.2 2. ANS: C OBJ: 10-1.1 Graphing Equations of Conic Sections STA: MI G1.7.2 3. ANS: A OBJ: 10-1.1 Graphing Equations of Conic Sections STA: MI G1.7.2 4. ANS: A OBJ: 10-1.1 Graphing Equations of Conic Sections STA: MI G1.7.2 5. ANS: C OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2 6. ANS: A OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2 7. ANS: A OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2 8. ANS: D OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2 9. ANS: B OBJ: 10-2.1 Writing the Equation of a Parabola 10. ANS: B OBJ: 10-2.1 Writing the Equation of a Parabola 11. ANS: C OBJ: 10-2.1 Writing the Equation of a Parabola 12. ANS: B OBJ: 10-2.1 Writing the Equation of a Parabola 13. ANS: D OBJ: 10-2.1 Writing the Equation of a Parabola 14. ANS: C OBJ: 10-2.2 Graphing Parabolas 15. ANS: D OBJ: 10-3.1 Writing the Equation of a Circle STA: MI G1.7.1 MI G1.7.2 16. ANS: C OBJ: 10-3.1 Writing the Equation of a Circle STA: MI G1.7.1 MI G1.7.2 17. ANS: B OBJ: 10-3.1 Writing the Equation of a Circle STA: MI G1.7.1 MI G1.7.2 18. ANS: A OBJ: 10-3.1 Writing the Equation of a Circle STA: MI G1.7.1 MI G1.7.2 19. ANS: A OBJ: 10-3.2 Using the Center and Radius of a Circle STA: MI G1.7.1 MI G1.7.2 20. ANS: C OBJ: 10-3.2 Using the Center and Radius of a Circle STA: MI G1.7.1 MI G1.7.2 21. ANS: D OBJ: 10-4.1 Writing the Equation of an Ellipse 22. ANS: A OBJ: 10-4.1 Writing the Equation of an Ellipse 23. ANS: A OBJ: 10-4.1 Writing the Equation of an Ellipse 24. ANS: B OBJ: 10-4.1 Writing the Equation of an Ellipse
25. ANS: D OBJ: 10-4.1 Writing the Equation of an Ellipse 26. ANS: C OBJ: 10-4.2 Finding and Using the Foci of an Ellipse 27. ANS: D OBJ: 10-5.1 Graphing Hyperbolas Centered at the Origin 28. ANS: A OBJ: 10-5.1 Graphing Hyperbolas Centered at the Origin