Question 1

Graph the parabola.
-$$x = - 2 ( y + 2 ) ^ { 2 } + 1$$

Accepted Answer

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

Question 2

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$

Question 3

Identify the type of graph.
-$$2 x ^ { 2 } - 4 x + 5 y ^ { 2 } + 30 y - 43 = 0$$

Accepted Answer

A)  The graph is a circle with center $( 1 , - 3 )$. 
B)  The graph is an ellipse with center $( 1 , - 3 )$. 
C)  The graph is the point $( - 1,3 )$. 
D)  The equation has no graph. 
A)  The graph is a circle with center $( 1 , - 3 )$. 
B)  The graph is an ellipse with center $( 1 , - 3 )$. 
C)  The graph is the point $( - 1,3 )$. 
D)  The equation has no graph.

Question 4

Solve the problem.
-A cross-section of an irrigation canal is a parabola. If the surface of the water is $40 \mathrm { ft }$ wide and the canal is $26 \mathrm { ft }$ deep at the center, how deep is it $1 \mathrm { ft }$ from the edge?

Accepted Answer

A)  $2.5 \mathrm { ft }$ 
B)  $1.3 \mathrm { ft }$ 
C)  $23.5 \mathrm { ft }$ 
D)  $24.7 \mathrm { ft }$ 
A)  $2.5 \mathrm { ft }$ 
B)  $1.3 \mathrm { ft }$ 
C)  $23.5 \mathrm { ft }$ 
D)  $24.7 \mathrm { ft }$

Question 5

Write an equation for the ellipse.
-minor axis from $( - 7 , - 1 )$ to $( - 1 , - 1 )$; major axis from $( - 4 , - 7 )$ to $( - 4,5 )$

Accepted Answer

A)  $\frac { ( x - 4 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 36 } = 1$ 
B)  $\frac { ( x + 4 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 9 } + \frac { ( y + 4 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 9 } + \frac { ( y - 6 ) ^ { 2 } } { 36 } = 1$ 
A)  $\frac { ( x - 4 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 36 } = 1$ 
B)  $\frac { ( x + 4 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 9 } + \frac { ( y + 4 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 9 } + \frac { ( y - 6 ) ^ { 2 } } { 36 } = 1$

Question 6

Solve the problem.
-A rectangular board is 8 by 9 units. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the
Length of the string.

Accepted Answer

A)  16 units 
B)  18 units 
C)  8 units 
D)  9 units 
A)  16 units 
B)  18 units 
C)  8 units 
D)  9 units

Question 7

Match the equation of the parabola with the appropriate description.
-$$y + 10 = 2 ( x - 15 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( - 15,5 )$ 
B)  Vertex at $( - 15,10 )$ 
C)  Vertex at $( 15 , - 10 )$ 
D)  Vertex at $( 30,10 )$ 
A)  Vertex at $( - 15,5 )$ 
B)  Vertex at $( - 15,10 )$ 
C)  Vertex at $( 15 , - 10 )$ 
D)  Vertex at $( 30,10 )$

Question 8

Graph the hyperbola.
-$4 y^{2}-36 x^{2}=144$

Accepted Answer

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

Question 9

Write the word or phrase that best completes each statement or answers the question.
-$$\text { Discuss the graph of the equation } \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \text { if } a = b \text {. }$$

Accepted Answer

If a = b, the graph

Question 10

Give the focus, directrix, and axis for the parabola.
-$$- \frac { 1 } { 24 } x ^ { 2 } = y$$

Accepted Answer

A)  $( 0 , - 6 ) , y = 6 , x$-axis 
B)  $( 0,6 ) , y = - 6 , y$-axis 
C)  $( - 12,0 ) , x = 6 , x$-axis 
D)  $( 0 , - 6 ) , \mathrm { y } = 6 , \mathrm { y }$-axis 
A)  $( 0 , - 6 ) , y = 6 , x$-axis 
B)  $( 0,6 ) , y = - 6 , y$-axis 
C)  $( - 12,0 ) , x = 6 , x$-axis 
D)  $( 0 , - 6 ) , \mathrm { y } = 6 , \mathrm { y }$-axis

Question 11

Solve the problem.
-A building has an entry the shape of a parabolic arch 4 ft high and 28 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Accepted Answer

A)  $x ^ { 2 } = - 196 y$ 
B)  $y ^ { 2 } = - 196 x$ 
C)  $y ^ { 2 } = - 49 x$ 
D)  $x ^ { 2 } = - 49 y$ 
A)  $x ^ { 2 } = - 196 y$ 
B)  $y ^ { 2 } = - 196 x$ 
C)  $y ^ { 2 } = - 49 x$ 
D)  $x ^ { 2 } = - 49 y$

Question 12

When a satellite is near Earth, its orbital trajectory may trace out a hyperbola, a parabola, or an ellipse. The type of trajectory depends on the satellite's velocity $V$ in meters per second. It will be hyperbolic if $V > \frac { k } { \sqrt { D } }$, parabolic if $V =$ $\frac { k } { \sqrt { D } }$, and elliptical if $V < \frac { k } { \sqrt { D } }$, where $k = 2.82 \times 10 ^ { 7 }$ is a constant and $\mathrm { D }$ is the distance in meters from the satellite to the center of Earth. Solve the problem.
-If a satellite is scheduled to leave Earthʹs gravitational influence, its velocity must be increased so that its trajectory changes from elliptical to hyperbolic. Determine the minimum increase in
Velocity necessary for a satellite traveling at a velocity of 4881 meters per second to escape Earthʹs
Gravitational influence when D = 194 × 106 m.

Accepted Answer

A)  4817 m per sec 
B)  4945 m per sec 
C)  6906 m per sec 
D)  -2856 m per sec 
A)  4817 m per sec 
B)  4945 m per sec 
C)  6906 m per sec 
D)  -2856 m per sec

Question 13

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

Accepted Answer

A)  $\mathrm { e } = \frac { 1 } { 2 }$ 
B)  $\mathrm { e } = 3$ 
C)  $\mathrm { e } = 1$ 
D)  $\mathrm { e } = 2$ 
A)  $\mathrm { e } = \frac { 1 } { 2 }$ 
B)  $\mathrm { e } = 3$ 
C)  $\mathrm { e } = 1$ 
D)  $\mathrm { e } = 2$

Question 14

Write the word or phrase that best completes each statement or answers the question.
-Explain why the graph of an ellipse does not satisfy the conditions for the graph of a
function.

Accepted Answer

The graph of an elli

Question 15

Give the focus, directrix, and axis for the parabola.
-$$( x + 2 ) ^ { 2 } = - 28 ( y - 3 )$$

Accepted Answer

A)  $( - 2 , - 4 ) , y = 10 , x = 3$ 
B)  $( - 2 , - 4 ) , y = 10 , x = 4$ 
C)  $( - 2 , - 4 ) , y = 10 , x = - 2$ 
D)  $( - 9 , - 4 ) , y = 10 , x = - 2$ 
A)  $( - 2 , - 4 ) , y = 10 , x = 3$ 
B)  $( - 2 , - 4 ) , y = 10 , x = 4$ 
C)  $( - 2 , - 4 ) , y = 10 , x = - 2$ 
D)  $( - 9 , - 4 ) , y = 10 , x = - 2$

Question 16

Write an equation for the parabola.
-vertex $( 7 , - 9 )$, focus $( 10 , - 9 )$

Accepted Answer

A)  $x - 7 = 3 ( y + 9 ) ^ { 2 }$ 
B)  $( y + 9 ) ^ { 2 } = 12 ( x - 7 )$ 
C)  $\frac { 3 } { 4 } ( x - 7 ) = ( y + 9 ) ^ { 2 }$ 
D)  $( x - 7 ) ^ { 2 } = 12 ( y + 9 )$ 
A)  $x - 7 = 3 ( y + 9 ) ^ { 2 }$ 
B)  $( y + 9 ) ^ { 2 } = 12 ( x - 7 )$ 
C)  $\frac { 3 } { 4 } ( x - 7 ) = ( y + 9 ) ^ { 2 }$ 
D)  $( x - 7 ) ^ { 2 } = 12 ( y + 9 )$

Question 17

Graph the conic section.
-

Accepted Answer

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

Question 18

Graph the hyperbola.
-$$\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$$

Accepted Answer

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

Question 19

Find the eccentricity of the hyperbola.
-$$x ^ { 2 } - 16 y ^ { 2 } = 1$$

Accepted Answer

A)  17 
B)  4 
C)  $\sqrt { 17 }$ 
D)  $\frac { \sqrt { 17 } } { 4 }$ 
A)  17 
B)  4 
C)  $\sqrt { 17 }$ 
D)  $\frac { \sqrt { 17 } } { 4 }$

Question 20

Fill in the blanks to complete the statement. The graph of $P ( x ) = 2 ( x - 8 ) ^ { 2 } - 4$ is a parabola with axis of symmetryــــــــــــ and vertexــــــــــــــــــــ

Accepted Answer

A)  $x = 2 ; ( - 8 , - 4 )$ 
B)  $x = 8 ; ( 8 , - 4 )$ 
C)  $( - 8 , - 4 ) ; x = - 8$ 
D)  $x = 8 ; ( - 8 , - 4 )$ 
A)  $x = 2 ; ( - 8 , - 4 )$ 
B)  $x = 8 ; ( 8 , - 4 )$ 
C)  $( - 8 , - 4 ) ; x = - 8$ 
D)  $x = 8 ; ( - 8 , - 4 )$

Graph the parabola. - $x = - 2 ( y + 2 ) ^ { 2 } + 1$ $Graph the parabola. - x = - 2 ( y + 2 ) ^ { 2 } + 1$

Choose the equation that matches the graph. -

Identify the type of graph. - $2 x ^ { 2 } - 4 x + 5 y ^ { 2 } + 30 y - 43 = 0$

Solve the problem. -A cross-section of an irrigation canal is a parabola. If the surface of the water is $40 \mathrm { ft }$ wide and the canal is $26 \mathrm { ft }$ deep at the center, how deep is it $1 \mathrm { ft }$ from the edge?

Write an equation for the ellipse. -minor axis from $( - 7 , - 1 )$ to $( - 1 , - 1 )$ ; major axis from $( - 4 , - 7 )$ to $( - 4,5 )$

Solve the problem. -A rectangular board is 8 by 9 units. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the Length of the string.

Match the equation of the parabola with the appropriate description. - $y + 10 = 2 ( x - 15 ) ^ { 2 }$

Graph the hyperbola. - $4 y^{2}-36 x^{2}=144$ $Graph the hyperbola. - 4 y^{2}-36 x^{2}=144$

Write the word or phrase that best completes each statement or answers the question. - $\text { Discuss the graph of the equation } \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \text { if } a = b \text {. }$

Give the focus, directrix, and axis for the parabola. - $- \frac { 1 } { 24 } x ^ { 2 } = y$

Solve the problem. -A building has an entry the shape of a parabolic arch 4 ft high and 28 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

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

Write the word or phrase that best completes each statement or answers the question. -Explain why the graph of an ellipse does not satisfy the conditions for the graph of a function.

Give the focus, directrix, and axis for the parabola. - $( x + 2 ) ^ { 2 } = - 28 ( y - 3 )$

Write an equation for the parabola. -vertex $( 7 , - 9 )$ , focus $( 10 , - 9 )$

Graph the conic section. -

Graph the hyperbola. - $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$

Find the eccentricity of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } = 1$

Fill in the blanks to complete the statement. The graph of $P ( x ) = 2 ( x - 8 ) ^ { 2 } - 4$ is a parabola with axis of symmetryــــــــــــ and vertexــــــــــــــــــــ

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

Exam 10: Analytic Geometry

Graph the parabola. - x=−2(y+2)2+1x = - 2 ( y + 2 ) ^ { 2 } + 1x=−2(y+2)2+1

Choose the equation that matches the graph. -

Identify the type of graph. - 2x2−4x+5y2+30y−43=02 x ^ { 2 } - 4 x + 5 y ^ { 2 } + 30 y - 43 = 02x2−4x+5y2+30y−43=0

Solve the problem. -A cross-section of an irrigation canal is a parabola. If the surface of the water is 40ft40 \mathrm { ft }40ft wide and the canal is 26ft26 \mathrm { ft }26ft deep at the center, how deep is it 1ft1 \mathrm { ft }1ft from the edge?

Write an equation for the ellipse. -minor axis from (−7,−1)( - 7 , - 1 )(−7,−1) to (−1,−1)( - 1 , - 1 )(−1,−1) ; major axis from (−4,−7)( - 4 , - 7 )(−4,−7) to (−4,5)( - 4,5 )(−4,5)

Solve the problem. -A rectangular board is 8 by 9 units. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the Length of the string.

Match the equation of the parabola with the appropriate description. - y+10=2(x−15)2y + 10 = 2 ( x - 15 ) ^ { 2 }y+10=2(x−15)2

Graph the hyperbola. - 4y2−36x2=1444 y^{2}-36 x^{2}=1444y2−36x2=144

Give the focus, directrix, and axis for the parabola. - −124x2=y- \frac { 1 } { 24 } x ^ { 2 } = y−241​x2=y

Solve the problem. -A building has an entry the shape of a parabolic arch 4 ft high and 28 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

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

Write the word or phrase that best completes each statement or answers the question. -Explain why the graph of an ellipse does not satisfy the conditions for the graph of a function.

Give the focus, directrix, and axis for the parabola. - (x+2)2=−28(y−3)( x + 2 ) ^ { 2 } = - 28 ( y - 3 )(x+2)2=−28(y−3)

Write an equation for the parabola. -vertex (7,−9)( 7 , - 9 )(7,−9) , focus (10,−9)( 10 , - 9 )(10,−9)

Graph the conic section. -

Graph the hyperbola. - y225−x236=1\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 125y2​−36x2​=1

Find the eccentricity of the hyperbola. - x2−16y2=1x ^ { 2 } - 16 y ^ { 2 } = 1x2−16y2=1

Fill in the blanks to complete the statement. The graph of P(x)=2(x−8)2−4P ( x ) = 2 ( x - 8 ) ^ { 2 } - 4P(x)=2(x−8)2−4 is a parabola with axis of symmetryــــــــــــ and vertexــــــــــــــــــــ

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

Graph the parabola. - $x = - 2 ( y + 2 ) ^ { 2 } + 1$ $Graph the parabola. - x = - 2 ( y + 2 ) ^ { 2 } + 1$

Identify the type of graph. - $2 x ^ { 2 } - 4 x + 5 y ^ { 2 } + 30 y - 43 = 0$

Solve the problem. -A cross-section of an irrigation canal is a parabola. If the surface of the water is $40 \mathrm { ft }$ wide and the canal is $26 \mathrm { ft }$ deep at the center, how deep is it $1 \mathrm { ft }$ from the edge?

Write an equation for the ellipse. -minor axis from $( - 7 , - 1 )$ to $( - 1 , - 1 )$ ; major axis from $( - 4 , - 7 )$ to $( - 4,5 )$

Match the equation of the parabola with the appropriate description. - $y + 10 = 2 ( x - 15 ) ^ { 2 }$

Graph the hyperbola. - $4 y^{2}-36 x^{2}=144$ $Graph the hyperbola. - 4 y^{2}-36 x^{2}=144$

Give the focus, directrix, and axis for the parabola. - $- \frac { 1 } { 24 } x ^ { 2 } = y$

Give the focus, directrix, and axis for the parabola. - $( x + 2 ) ^ { 2 } = - 28 ( y - 3 )$

Write an equation for the parabola. -vertex $( 7 , - 9 )$ , focus $( 10 , - 9 )$

Graph the hyperbola. - $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$

Find the eccentricity of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } = 1$

Fill in the blanks to complete the statement. The graph of $P ( x ) = 2 ( x - 8 ) ^ { 2 } - 4$ is a parabola with axis of symmetryــــــــــــ and vertexــــــــــــــــــــ