Question 1

Write an equation for the parabola with vertex at the origin.
-Through $( \sqrt { 2 } , 2 )$, opening upward

Accepted Answer

A)  $x = y ^ { 2 }$ 
B)  $x = \frac { \sqrt { 2 } } { 2 } y ^ { 2 }$ 
C)  $y = x ^ { 2 }$ 
D)  $y = 2 x ^ { 2 }$ 
A)  $x = y ^ { 2 }$ 
B)  $x = \frac { \sqrt { 2 } } { 2 } y ^ { 2 }$ 
C)  $y = x ^ { 2 }$ 
D)  $y = 2 x ^ { 2 }$

Question 2

Find the eccentricity of the conic section shown in the graph.
-

Accepted Answer

A)  $\mathrm { e } = \frac { \sqrt { 17 } } { 4 }$ 
B)  $e = \frac { 4 } { \sqrt { 17 } }$ 
C)  $\mathrm { e } = 1$ 
D)  $\mathrm { e } = 4$ 
A)  $\mathrm { e } = \frac { \sqrt { 17 } } { 4 }$ 
B)  $e = \frac { 4 } { \sqrt { 17 } }$ 
C)  $\mathrm { e } = 1$ 
D)  $\mathrm { e } = 4$

Question 3

Identify the type of graph.
-$$( x + 6 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + 12 = 0$$

Accepted Answer

A)  The graph is the point $( - 6,4 )$. 
B)  The equation has no graph. 
C)  The graph is a circle with center $( - 6,4 )$. 
D)  The graph is an ellipse with center $( 6 , - 4 )$. 
A)  The graph is the point $( - 6,4 )$. 
B)  The equation has no graph. 
C)  The graph is a circle with center $( - 6,4 )$. 
D)  The graph is an ellipse with center $( 6 , - 4 )$.

Question 4

Identify the type of graph.
-$$2 x ^ { 2 } + 20 x + 2 y ^ { 2 } - 36 y = - 211$$

Accepted Answer

A)  The graph is a circle with center $( 5 , - 9 )$. 
B)  The graph is a circle with center $( - 5,9 )$. 
C)  The graph is the point $( - 5,9 )$. 
D)  The equation has no graph. 
A)  The graph is a circle with center $( 5 , - 9 )$. 
B)  The graph is a circle with center $( - 5,9 )$. 
C)  The graph is the point $( - 5,9 )$. 
D)  The equation has no graph.

Question 5

Write an equation for the hyperbola.
-vertices at $( - 4,3 )$ and $( 2,3 )$, passing through the point $( - 6,9 )$

Accepted Answer

A)  $\frac { ( x + 1 ) ^ { 2 } } { 9 } - \frac { ( y - 3 ) ^ { 2 } } { \frac { 117 } { 4 } } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 9 } - \frac { ( y - 3 ) ^ { 2 } } { \frac { 81 } { 4 } } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { \frac { 117 } { 4 } } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { \frac { 81 } { 4 } } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$ 
A)  $\frac { ( x + 1 ) ^ { 2 } } { 9 } - \frac { ( y - 3 ) ^ { 2 } } { \frac { 117 } { 4 } } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 9 } - \frac { ( y - 3 ) ^ { 2 } } { \frac { 81 } { 4 } } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { \frac { 117 } { 4 } } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { \frac { 81 } { 4 } } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$

Question 6

Identify the type of graph.
-$$\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 3 }$$

Accepted Answer

A)  The graph is an ellipse with foci on the $y$-axis. 
B)  The graph is a hyperbola with foci on the $x$-axis 
C)  The graph is a hyperbola with foci on the $y$-axis 
D)  The graph is an ellipse with foci on the x-axis. 
A)  The graph is an ellipse with foci on the $y$-axis. 
B)  The graph is a hyperbola with foci on the $x$-axis 
C)  The graph is a hyperbola with foci on the $y$-axis 
D)  The graph is an ellipse with foci on the x-axis.

Question 7

Find the eccentricity of the conic section shown in the graph.
-

Accepted Answer

A)  $\mathrm { e } = 1$ 
B)  $e = \frac { 21 } { 5 }$ 
C)  $\mathrm { e } = \frac { \sqrt { 29 } } { 5 }$ 
D)  $\mathrm { e } = \frac { 29 } { 2 }$ 
A)  $\mathrm { e } = 1$ 
B)  $e = \frac { 21 } { 5 }$ 
C)  $\mathrm { e } = \frac { \sqrt { 29 } } { 5 }$ 
D)  $\mathrm { e } = \frac { 29 } { 2 }$

Question 8

Solve the problem.
-If an object is thrown upward with an initial velocity of $11 \mathrm { ft }$ per second, then its height is given by $h = - 11 t ^ { 2 } + 44 t$. What is its maximum height?

Accepted Answer

A)  $44 \mathrm { ft }$ 
B)  $33 \mathrm { ft }$ 
C)  $66 \mathrm { ft }$ 
D)  $22 \mathrm { ft }$ 
A)  $44 \mathrm { ft }$ 
B)  $33 \mathrm { ft }$ 
C)  $66 \mathrm { ft }$ 
D)  $22 \mathrm { ft }$

Question 9

Match the equation of the parabola with the appropriate description.
-$$y = - 6 x ^ { 2 } + 2 x + 2$$

Accepted Answer

A)  Opens right 
B)  Opens up 
C)  Opens left 
D)  Opens down 
A)  Opens right 
B)  Opens up 
C)  Opens left 
D)  Opens down

Question 10

Provide an appropriate response.
-In the ellipse $\frac { ( y + 5 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$, what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Accepted Answer

A)  Horizontal: $y = 9$; Vertical: $x = - 5$ 
B)  Horizontal: $y = 5$; Vertical: $x = - 9$ 
C)  Horizontal: $y = - 5$; Vertical: $x = 9$ 
D)  Horizontal: $y = 5$; Vertical: $x = 9$ 
A)  Horizontal: $y = 9$; Vertical: $x = - 5$ 
B)  Horizontal: $y = 5$; Vertical: $x = - 9$ 
C)  Horizontal: $y = - 5$; Vertical: $x = 9$ 
D)  Horizontal: $y = 5$; Vertical: $x = 9$

Question 11

Match the equation of the parabola with the appropriate description.
-$$x + 3 = 2 ( y + 9 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( 9,3 )$ 
B)  Vertex at $( - 9 , - 3 )$ 
C)  Vertex at $( - 3 , - 9 )$ 
D)  Vertex at $( 3,9 )$ 
A)  Vertex at $( 9,3 )$ 
B)  Vertex at $( - 9 , - 3 )$ 
C)  Vertex at $( - 3 , - 9 )$ 
D)  Vertex at $( 3,9 )$

Question 12

Find the eccentricity of the conic section shown in the graph.
-

Accepted Answer

A)  $e = \frac { 4 \sqrt { 3 } } { 3 }$ 
B)  $e = 1$ 
C)  $\mathrm { e } = \frac { \sqrt { 3 } } { 4 }$ 
D)  $\mathrm { e } = \sqrt { 3 }$ 
A)  $e = \frac { 4 \sqrt { 3 } } { 3 }$ 
B)  $e = 1$ 
C)  $\mathrm { e } = \frac { \sqrt { 3 } } { 4 }$ 
D)  $\mathrm { e } = \sqrt { 3 }$

Question 13

Write an equation for the ellipse.
-foci at $( - 1,7 ) , ( - 1,1 )$; major axis length of 10

Accepted Answer

A)  $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 1 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1$ 
A)  $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 1 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1$

Question 14

Identify the type of graph.
-$$- 4 x ^ { 2 } + 16 x + 5 y ^ { 2 } - 80 y - 16 = - 320$$

Accepted Answer

A)  The equation has no graph. 
B)  The graph is the point $( 2,8 )$. 
C)  The graph is a circle with center $( 2,8 )$. 
D)  The graph is a hyperbola opening upward and downward. 
A)  The equation has no graph. 
B)  The graph is the point $( 2,8 )$. 
C)  The graph is a circle with center $( 2,8 )$. 
D)  The graph is a hyperbola opening upward and downward.

Question 15

Write an equation for the parabola with vertex at the origin.
-Through $( 9,9 )$, symmetric with respect to the $y$-axis

Accepted Answer

A)  $x ^ { 2 } = 9 y$ 
B)  $y = 9 x ^ { 2 }$ 
C)  $x = - 9 y ^ { 2 }$ 
D)  $y ^ { 2 } = 9 x$ 
A)  $x ^ { 2 } = 9 y$ 
B)  $y = 9 x ^ { 2 }$ 
C)  $x = - 9 y ^ { 2 }$ 
D)  $y ^ { 2 } = 9 x$

Question 16

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( 0,11 )$ is twice the distance from the line $y = 7$.

Accepted Answer

A)  Ellipse 
B)  Circle 
C)  Parabola 
D)  Hyperbola 
A)  Ellipse 
B)  Circle 
C)  Parabola 
D)  Hyperbola

Question 17

Graph the parabola.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Find the center, foci, and asymptotes of the hyperbola.
-$$x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$$

Accepted Answer

A)  C: $( 4,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 4 } \mathrm { x }$ 
B)  C: $( 0,0 ) ; F : ( 4,0 ) , ( - 4,0 ) ; A : y = \frac { 1 } { 4 } x , y = - \frac { 1 } { 4 } x$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = 4 \mathrm { x } , \mathrm { y } = - 4 \mathrm { x }$ 
D)  $\mathrm { C } : ( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 5 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 5 } \mathrm { x }$ 
A)  C: $( 4,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 4 } \mathrm { x }$ 
B)  C: $( 0,0 ) ; F : ( 4,0 ) , ( - 4,0 ) ; A : y = \frac { 1 } { 4 } x , y = - \frac { 1 } { 4 } x$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = 4 \mathrm { x } , \mathrm { y } = - 4 \mathrm { x }$ 
D)  $\mathrm { C } : ( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 5 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 5 } \mathrm { x }$

Question 19

Write an equation for the parabola.
-vertex: $( 3 , - 4 )$, directrix: $x = 11$

Accepted Answer

A)  $( x + 4 ) ^ { 2 } = - 32 ( y - 3 )$ 
B)  $x ^ { 2 } = - 32 ( y - 3 )$ 
C)  $( y + 4 ) ^ { 2 } = - 32 ( x - 3 )$ 
D)  $( y - 3 ) ^ { 2 } = - 32 ( x + 4 )$ 
A)  $( x + 4 ) ^ { 2 } = - 32 ( y - 3 )$ 
B)  $x ^ { 2 } = - 32 ( y - 3 )$ 
C)  $( y + 4 ) ^ { 2 } = - 32 ( x - 3 )$ 
D)  $( y - 3 ) ^ { 2 } = - 32 ( x + 4 )$

Question 20

Solve the problem.
-The roof of a building is in the shape of the hyperbola $$y ^ { 2 } - x ^ { 2 } = 22$$ where x and y are in meters. Refer to the figure and determine the height h of the outside walls. $$\mathrm { A } = 9 \mathrm {~m}$$

Accepted Answer

A)  $103 \mathrm {~m}$ 
B)  $59 \mathrm {~m}$ 
C)  $10.1 \mathrm {~m}$ 
D)  $13 \mathrm {~m}$ 13 
A)  $103 \mathrm {~m}$ 
B)  $59 \mathrm {~m}$ 
C)  $10.1 \mathrm {~m}$ 
D)  $13 \mathrm {~m}$ 13

Write an equation for the parabola with vertex at the origin. -Through $( \sqrt { 2 } , 2 )$ , opening upward

Find the eccentricity of the conic section shown in the graph. -

Identify the type of graph. - $( x + 6 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + 12 = 0$

Identify the type of graph. - $2 x ^ { 2 } + 20 x + 2 y ^ { 2 } - 36 y = - 211$

Write an equation for the hyperbola. -vertices at $( - 4,3 )$ and $( 2,3 )$ , passing through the point $( - 6,9 )$

Identify the type of graph. - $\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 3 }$

Find the eccentricity of the conic section shown in the graph. -

Solve the problem. -If an object is thrown upward with an initial velocity of $11 \mathrm { ft }$ per second, then its height is given by $h = - 11 t ^ { 2 } + 44 t$ . What is its maximum height?

Match the equation of the parabola with the appropriate description. - $y = - 6 x ^ { 2 } + 2 x + 2$

Provide an appropriate response. -In the ellipse $\frac { ( y + 5 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$ , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Match the equation of the parabola with the appropriate description. - $x + 3 = 2 ( y + 9 ) ^ { 2 }$

Find the eccentricity of the conic section shown in the graph. -

Write an equation for the ellipse. -foci at $( - 1,7 ) , ( - 1,1 )$ ; major axis length of 10

Identify the type of graph. - $- 4 x ^ { 2 } + 16 x + 5 y ^ { 2 } - 80 y - 16 = - 320$

Write an equation for the parabola with vertex at the origin. -Through $( 9,9 )$ , symmetric with respect to the $y$ -axis

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( 0,11 )$ is twice the distance from the line $y = 7$ .

Graph the parabola. -

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$

Write an equation for the parabola. -vertex: $( 3 , - 4 )$ , directrix: $x = 11$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

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Exam 10: Analytic Geometry

Write an equation for the parabola with vertex at the origin. -Through (2,2)( \sqrt { 2 } , 2 )(2​,2) , opening upward

Find the eccentricity of the conic section shown in the graph. -

Identify the type of graph. - (x+6)2+(y−4)2+12=0( x + 6 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + 12 = 0(x+6)2+(y−4)2+12=0

Identify the type of graph. - 2x2+20x+2y2−36y=−2112 x ^ { 2 } + 20 x + 2 y ^ { 2 } - 36 y = - 2112x2+20x+2y2−36y=−211

Write an equation for the hyperbola. -vertices at (−4,3)( - 4,3 )(−4,3) and (2,3)( 2,3 )(2,3) , passing through the point (−6,9)( - 6,9 )(−6,9)

Identify the type of graph. - x29=1−y23\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 3 }9x2​=1−3y2​

Find the eccentricity of the conic section shown in the graph. -

Solve the problem. -If an object is thrown upward with an initial velocity of 11ft11 \mathrm { ft }11ft per second, then its height is given by h=−11t2+44th = - 11 t ^ { 2 } + 44 th=−11t2+44t . What is its maximum height?

Match the equation of the parabola with the appropriate description. - y=−6x2+2x+2y = - 6 x ^ { 2 } + 2 x + 2y=−6x2+2x+2

Provide an appropriate response. -In the ellipse (y+5)236+(x−9)216=1\frac { ( y + 5 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 136(y+5)2​+16(x−9)2​=1 , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Match the equation of the parabola with the appropriate description. - x+3=2(y+9)2x + 3 = 2 ( y + 9 ) ^ { 2 }x+3=2(y+9)2

Find the eccentricity of the conic section shown in the graph. -

Write an equation for the ellipse. -foci at (−1,7),(−1,1)( - 1,7 ) , ( - 1,1 )(−1,7),(−1,1) ; major axis length of 10

Identify the type of graph. - −4x2+16x+5y2−80y−16=−320- 4 x ^ { 2 } + 16 x + 5 y ^ { 2 } - 80 y - 16 = - 320−4x2+16x+5y2−80y−16=−320

Write an equation for the parabola with vertex at the origin. -Through (9,9)( 9,9 )(9,9) , symmetric with respect to the yyy -axis

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point (0,11)( 0,11 )(0,11) is twice the distance from the line y=7y = 7y=7 .

Graph the parabola. -

Find the center, foci, and asymptotes of the hyperbola. - x2−y216=1x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1x2−16y2​=1

Write an equation for the parabola. -vertex: (3,−4)( 3 , - 4 )(3,−4) , directrix: x=11x = 11x=11

Solve the problem. -The roof of a building is in the shape of the hyperbola y2−x2=22y ^ { 2 } - x ^ { 2 } = 22y2−x2=22 where x and y are in meters. Refer to the figure and determine the height h of the outside walls. A=9 m\mathrm { A } = 9 \mathrm {~m}A=9 m

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Further Topics in Algebra

Review of Basic Concepts

Filters

Write an equation for the parabola with vertex at the origin. -Through $( \sqrt { 2 } , 2 )$ , opening upward

Identify the type of graph. - $( x + 6 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + 12 = 0$

Identify the type of graph. - $2 x ^ { 2 } + 20 x + 2 y ^ { 2 } - 36 y = - 211$

Write an equation for the hyperbola. -vertices at $( - 4,3 )$ and $( 2,3 )$ , passing through the point $( - 6,9 )$

Identify the type of graph. - $\frac { x ^ { 2 } } { 9 } = 1 - \frac { y ^ { 2 } } { 3 }$

Solve the problem. -If an object is thrown upward with an initial velocity of $11 \mathrm { ft }$ per second, then its height is given by $h = - 11 t ^ { 2 } + 44 t$ . What is its maximum height?

Match the equation of the parabola with the appropriate description. - $y = - 6 x ^ { 2 } + 2 x + 2$

Provide an appropriate response. -In the ellipse $\frac { ( y + 5 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$ , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Match the equation of the parabola with the appropriate description. - $x + 3 = 2 ( y + 9 ) ^ { 2 }$

Write an equation for the ellipse. -foci at $( - 1,7 ) , ( - 1,1 )$ ; major axis length of 10

Identify the type of graph. - $- 4 x ^ { 2 } + 16 x + 5 y ^ { 2 } - 80 y - 16 = - 320$

Write an equation for the parabola with vertex at the origin. -Through $( 9,9 )$ , symmetric with respect to the $y$ -axis

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( 0,11 )$ is twice the distance from the line $y = 7$ .

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1$

Write an equation for the parabola. -vertex: $( 3 , - 4 )$ , directrix: $x = 11$