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.
The graph is a circle of radius 5. Its center
is at the origin. The y-axis and the x-axis
are lines of symmetry.
b.
d.
The graph is a circle of radius 25. Its
center is at the origin. Every line through
the center is a line of symmetry.
2.
The graph is a circle of radius 25. Its
center is at the origin. The y-axis and the
x-axis are lines of symmetry.
The graph is a circle of radius 5. Its center
is at the origin. Every line through the
center is a line of symmetry.
a.
The
c.
graph is an ellipse. The center is at the
origin. It has two lines of symmetry, the
x-axis and the y-axis.
graph is a circle. The center is at the origin.
Every line through the origin is a line of
symmetry.
b.
The
d.
The
graph is a circle. The center is at the origin.
Every line through the origin is a line of
symmetry.
graph is an ellipse. The center is at the
origin. It has two lines of symmetry, the
x-axis and the y-axis.
3.
a.
The
c.
The 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.
b.
The graph is a circle with radius 9. Its
center is at the origin. Every line through
the center is a line of symmetry.
d.
The 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
a.
The 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.
. Find the domain and range.
c.
The
domain is all real numbers.The range is
.
The
domain is
range is
. The
.
b.
The
domain is
range is all real numbers.
. The
d.
The
domain is
is
. The range
.
Identify the center and intercepts of the conic section. Then find the domain and range.
5.
a. The center of the ellipse is (0, 0). The x-intercepts are (–5, 0) and (5, 0). The y-intercepts
are (0, 9) and (0, –9). The domain is {x | –9 ≤ y ≤ 9}. The range is {y | –5 ≤ x ≤ 5}.
b. The center of the ellipse is (0, 0). The x-intercepts are (0, 9) and (0, –9). The y-intercepts
are (–5, 0) and (5, 0). The domain is {x | –5 ≤ x ≤ 5}. The range is {y | –9 ≤ y ≤ 9}.
c. The center of the ellipse is (0, 0). The x-intercepts are (–5, 0) and (5, 0). The y-intercepts
are (0, 9) and (0, –9). The domain is {x | –5 ≤ x ≤ 5}. The range is {y | –9 ≤ y ≤ 9}.
d. The center of the ellipse is (0, 0). The x-intercepts are (0, 9) and (0, –9). The y-intercepts
are (–5, 0) and (5, 0). The domain is {x | –9 ≤ y ≤ 9}. The range is {y | –5 ≤ x ≤ 5}.
6.
a. The center of the hyperbola is (0, 0). The y-intercepts are (0, 2) and (0, –2). The domain is
all real numbers. The range is {y | y ≤ –2 or y ≥ 2}.
b. The center of the hyperbola is (0, 0). The y-intercepts are (0, 2) and (0, –2). The domain is
all real numbers. The range is {y | y ≥ –2 or y ≤ 2}.
c. The center of the hyperbola is (0, 0). The x-intercepts are (0, 2) and (0, –2). The domain is
all real numbers. The range is {x | x ≤ –2 or x ≥ 2}.
d. The center of the hyperbola is (0, 0). The x-intercepts are (0, 2) and (0, –2). The domain is
all real numbers. The range is {y | y ≤ –2 or y ≥ 2}.
7.
a. The center of the circle is (0, 0). The x-intercepts are (9, 0) and (–9, 0). The y-intercepts
are (0, 9) and (0, –9). The domain is {x | –9 ≤ x ≤ 9}. The range is {y | –9 ≤ y ≤ 9}.
b. The center of the circle is (0, 0). The x-intercepts are (9, 0) and (–9, 0). The y-intercepts
are (0, 9) and (0, –9). The domain is {y | 9 ≤ y ≤ –9}. The range is {x | 9 ≤ x ≤ –9}.
c. The center of the circle is (9, 9). The x-intercepts are (9, 0) and (–9, 0). The y-intercepts
are (0, 9) and (0, –9). The domain is {y | 9 ≤ y ≤ –9}. The range is {x | 9 ≤ x ≤ –9}.
d. The center of the circle is (9, 9). The x-intercepts are (9, 0) and (–9, 0). The y-intercepts
are (0, 9) and (0, –9). The domain is {x | –9 ≤ x ≤ 9}. The 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.
a.
b.
c.
d.
9. Write an equation of a parabola with a vertex at the origin and a focus at (–7, 0).
a.
c.
b.
d.
10. A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.
The 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.
a.
c.
b.
d.
11. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.
a.
c.
b.
d.
12. Use the graph to write an equation for the parabola.
a.
c.
b.
d.
13. Which is the equation of the parabola that has a vertex at the origin and a focus at (3, 0)?
a.
c.
b.
14. Graph
a.
d.
.
c.
b.
d.
15. Write an equation of a circle with center (–7, 4) and radius 7.
a.
c.
b.
16. Write an equation for the translation of
a.
b.
d.
, 7 units left and 5 units up.
c.
d.
17. Write an equation in standard form for the circle.
a.
c.
b.
d.
18. A satellite is launched in a circular orbit around Earth at an altitude of 100 miles above the surface. The
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).
a.
c.
b.
d.
19. Find the center and radius of the circle with equation
a. (1, –5); 8
b. (–1, 5); 8
20. Graph
.
c. (1, –5); 64
d. (–1, 5); 64
.
a.
c.
b.
d.
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.
a.
c.
b.
d.
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.
a.
c.
b.
d.
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)
a.
c.
b.
d.
24. height of 12 units and width of 19 units
a.
b.
25. height of 4 units and width of 5 units
a.
b.
c.
d.
c.
d.
26. Write an equation for the graph.
a.
c.
b.
d.
Graph the conic section.
27.
a.
c.
b.
d.
a.
c.
28.
b.
d.
Algebra II B Review 3
Answer Section
MULTIPLE CHOICE
1. ANS:
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D
OBJ: 10-1.1 Graphing Equations of Conic Sections
MI G1.7.2
C
OBJ: 10-1.1 Graphing Equations of Conic Sections
MI G1.7.2
A
OBJ: 10-1.1 Graphing Equations of Conic Sections
MI G1.7.2
A
OBJ: 10-1.1 Graphing Equations of Conic Sections
MI G1.7.2
C
OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2
A
OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2
A
OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2
D
OBJ: 10-1.2 Identifying Conic Sections STA: MI G1.7.2
B
OBJ: 10-2.1 Writing the Equation of a Parabola
MI G1.7.4
B
OBJ: 10-2.1 Writing the Equation of a Parabola
MI G1.7.4
C
OBJ: 10-2.1 Writing the Equation of a Parabola
MI G1.7.4
B
OBJ: 10-2.1 Writing the Equation of a Parabola
MI G1.7.4
D
OBJ: 10-2.1 Writing the Equation of a Parabola
MI G1.7.4
C
OBJ: 10-2.2 Graphing Parabolas
STA: MI G1.7.4
D
OBJ: 10-3.1 Writing the Equation of a Circle
MI G1.7.1 | MI G1.7.2
C
OBJ: 10-3.1 Writing the Equation of a Circle
MI G1.7.1 | MI G1.7.2
B
OBJ: 10-3.1 Writing the Equation of a Circle
MI G1.7.1 | MI G1.7.2
A
OBJ: 10-3.1 Writing the Equation of a Circle
MI G1.7.1 | MI G1.7.2
A
OBJ: 10-3.2 Using the Center and Radius of a Circle
MI G1.7.1 | MI G1.7.2
C
OBJ: 10-3.2 Using the Center and Radius of a Circle
MI G1.7.1 | MI G1.7.2
D
OBJ: 10-4.1 Writing the Equation of an Ellipse
MI G1.7.4
A
OBJ: 10-4.1 Writing the Equation of an Ellipse
MI G1.7.4
A
OBJ: 10-4.1 Writing the Equation of an Ellipse
MI G1.7.4
B
OBJ: 10-4.1 Writing the Equation of an Ellipse
MI G1.7.4
25. ANS:
STA:
26. ANS:
STA:
27. ANS:
STA:
28. ANS:
STA:
D
MI G1.7.4
C
MI G1.7.4
D
MI G1.7.4
A
MI G1.7.4
OBJ: 10-4.1 Writing the Equation of an Ellipse
OBJ: 10-4.2 Finding and Using the Foci of an Ellipse
OBJ: 10-5.1 Graphing Hyperbolas Centered at the Origin
OBJ: 10-5.1 Graphing Hyperbolas Centered at the Origin