Question 1

Give the focus, directrix, and axis for the parabola.
-$( y - 6 ) ^ { 2 } = - 12 ( x + 2 )$

Accepted Answer

A)  $( - 5,6 ) , x = 1 , y = - 2$ 
B)  $( - 5,6 ) , x = - 2 , y = 6$ 
C)  $( - 5,6 ) , x = 1 , y = 6$ 
D)  $( - 5,3 ) , x = 1 , y = 6$ 
A)  $( - 5,6 ) , x = 1 , y = - 2$ 
B)  $( - 5,6 ) , x = - 2 , y = 6$ 
C)  $( - 5,6 ) , x = 1 , y = 6$ 
D)  $( - 5,3 ) , x = 1 , y = 6$ C

Question 2

Identify the type of graph.
-$x ^ { 2 } - 9 x + y = 0$

Accepted Answer

A)  The graph is an ellipse with center (0, 9). 
B)  The equation has no graph. 
C)  The graph is a parabola opening downward. 
D)  The graph is a parabola opening upward. 
A)  The graph is an ellipse with center (0, 9). 
B)  The equation has no graph. 
C)  The graph is a parabola opening downward. 
D)  The graph is a parabola opening upward. C

Question 3

Graph the equation. Give the domain and range. Identify whether the equation is a function.
-$4 y=\sqrt{3 x^{2}-12}$

Accepted Answer

A) 
 
$( \infty , - 2 ] \cup [ 2 , \infty ) ; ( \infty , 0 ]$; function 
B) 
11ed7d40_c984_dd8f_8ff5_
87e2357da8a0_TB7514_11

$( \infty , - 2 ] \cup [ 2 , \infty ) ; [ 0 , \infty )$; function 
C) 
 
$( \infty , - 2 ] \cup [ 2 , \infty ) ; [ 0 , \infty )$; not a function 
D)

$( \infty , - 2 ] \cup [ 2 , \infty ) ; ( \infty , 0 ] ;$ not a function 
A) 
 
$( \infty , - 2 ] \cup [ 2 , \infty ) ; ( \infty , 0 ]$; function 
B) 
11ed7d40_c984_dd8f_8ff5_
87e2357da8a0_TB7514_11

$( \infty , - 2 ] \cup [ 2 , \infty ) ; [ 0 , \infty )$; function 
C) 
 
$( \infty , - 2 ] \cup [ 2 , \infty ) ; [ 0 , \infty )$; not a function 
D)

$( \infty , - 2 ] \cup [ 2 , \infty ) ; ( \infty , 0 ] ;$ not a function B

Question 4

Graph the parabola.
-$$x = ( y + 5 ) ^ { 2 } + 6$$

Accepted Answer

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

Question 5

Provide an appropriate response.
-$$\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1 \text { are } ( 2,0 ) \text { and } ( - 2,0 )$$ The x-intercepts of the hyperbola with equation

Accepted Answer

A) True 
 B)False

Question 6

Write an equation for the ellipse.
-$\mathrm { x }$-intercepts $( \pm 6,0 ) ; \mathrm { y }$-intercepts $( 0 , \pm 3 )$

Accepted Answer

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

Question 7

Write an equation for the parabola with vertex at the origin.
-Focus $\left( - \frac { 1 } { 7 } , 0 \right)$

Accepted Answer

A)  $y ^ { 2 } = - 28 x$ 
B)  $y ^ { 2 } = - \frac { 4 } { 7 } x$ 
C)  $x ^ { 2 } = - \frac { 4 } { 7 } y$ 
D)  $x ^ { 2 } = - 28 y$ 
A)  $y ^ { 2 } = - 28 x$ 
B)  $y ^ { 2 } = - \frac { 4 } { 7 } x$ 
C)  $x ^ { 2 } = - \frac { 4 } { 7 } y$ 
D)  $x ^ { 2 } = - 28 y$

Question 8

Provide an appropriate response.
-Explain in your own words how you can tell from the equation whether a parabola opens 
up or down or whether it opens left or right.

Accepted Answer

The parabola opens up or down

Question 9

Write an equation for the hyperbola.
-$x$-intercepts $( \pm 5,0 )$; center at origin; passing through $( 5 \sqrt { 5 } , 6 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$

Question 10

Graph the conic section.
-$$25 ( x - 5 ) ^ { 2 } + 16 ( y - 2 ) ^ { 2 } = 400$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Question 11

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 sum of the distances from the points (4, 0) and (-4, 0) is 28.

Accepted Answer

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

Question 12

Provide an appropriate response.
-  Using only this graph of $f ( x ) = a ( x - h ) ^ { 2 } + k$, what are the signs of $h$ and $k$ ?

Accepted Answer

A)  Both are negative. 
B)  $h$ is positive and $k$ is negative. 
C)  Both are positive.
$\mathrm { D } ) \mathrm { h }$ is negative and $\mathrm { k }$ is positive. 
A)  Both are negative. 
B)  $h$ is positive and $k$ is negative. 
C)  Both are positive.
$\mathrm { D } ) \mathrm { h }$ is negative and $\mathrm { k }$ is positive.

Question 13

Match the equation of the ellipse with the appropriate description.
-$16 x ^ { 2 } + 49 y ^ { 2 } = 3136$

Accepted Answer

A)  $x$-intercepts $( 14,0 ) , ( - 14,0 )$; $y$-intercepts $( 0,8 ) , ( 0 , - 8 )$ 
B)  $x$-intercepts $( 64,0 ) , ( - 64,0 )$; y-intercepts $( 0,196 ) , ( 0 , - 196 )$ 
C)  $x$-intercepts $( 196,0 ) , ( - 196,0 )$; y-intercepts $( 0,64 ) , ( 0 , - 64 )$ 
D)  x-intercepts $( 8,0 ) , ( - 8,0 )$; y-intercepts $( 0,14 ) , ( 0 , - 14 )$ 
A)  $x$-intercepts $( 14,0 ) , ( - 14,0 )$; $y$-intercepts $( 0,8 ) , ( 0 , - 8 )$ 
B)  $x$-intercepts $( 64,0 ) , ( - 64,0 )$; y-intercepts $( 0,196 ) , ( 0 , - 196 )$ 
C)  $x$-intercepts $( 196,0 ) , ( - 196,0 )$; y-intercepts $( 0,64 ) , ( 0 , - 64 )$ 
D)  x-intercepts $( 8,0 ) , ( - 8,0 )$; y-intercepts $( 0,14 ) , ( 0 , - 14 )$

Question 14

Provide an appropriate response.
-An ellipse has eccentricity between 0 and 1. 114)

Accepted Answer

A) True 
 B)False

Question 15

Find the eccentricity e of the hyperbola.
-$$x ^ { 2 } - 2 y ^ { 2 } = 6$$

Accepted Answer

A)  $\sqrt { 6 }$ 
B)  $\frac { \sqrt { 6 } } { 2 }$ 
C)  $\sqrt { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$ 
A)  $\sqrt { 6 }$ 
B)  $\frac { \sqrt { 6 } } { 2 }$ 
C)  $\sqrt { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$

Question 16

Find the eccentricity e of the hyperbola.
-$x ^ { 2 } - y ^ { 2 } = 49$

Accepted Answer

A)  $\sqrt { 7 }$ 
B)  1 
C)  0 
D)  $\sqrt { 2 }$ 
A)  $\sqrt { 7 }$ 
B)  1 
C)  0 
D)  $\sqrt { 2 }$

Question 17

Write an equation for the parabola with vertex at the origin.
-Focus $( 0,7 )$

Accepted Answer

A)  $y ^ { 2 } = 7 x$ 
B)  $x ^ { 2 } = 28 y$ 
C)  $y ^ { 2 } = 28 x$ 
D)  $x ^ { 2 } = 7 y$ 
A)  $y ^ { 2 } = 7 x$ 
B)  $x ^ { 2 } = 28 y$ 
C)  $y ^ { 2 } = 28 x$ 
D)  $x ^ { 2 } = 7 y$

Question 18

Write an equation for the ellipse.
-foci at $( - 6 , - 3 ) , ( 0 , - 3 )$; major axis length of 10

Accepted Answer

A)  $\frac { ( \mathrm { x } + 4 ) ^ { 2 } } { 25 } + \frac { ( \mathrm { y } - 3 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 3 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( y + 4 ) ^ { 2 } } { 25 } + \frac { ( x + 3 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 3 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$ 
A)  $\frac { ( \mathrm { x } + 4 ) ^ { 2 } } { 25 } + \frac { ( \mathrm { y } - 3 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 3 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( y + 4 ) ^ { 2 } } { 25 } + \frac { ( x + 3 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 3 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$

Question 19

Graph the equation. Give the domain and range. Identify whether the equation is a function.
-$$y = - \sqrt { 1 - \frac { x ^ { 2 } } { 64 } }$$

Accepted Answer

A) 
 
$[ - 8,8 ] ; [ - 8,0 ]$; function 
B)

$[ - 8,8 ] ; [ 0,1 ]$; not a function 
C) 
  
D) 
 
 $[ - 8,8 ] ; [ 0,8 ] ;$ not a function
$[ - 8,8 ] ; [ - 1,0 ]$; function 
A) 
 
$[ - 8,8 ] ; [ - 8,0 ]$; function 
B)

$[ - 8,8 ] ; [ 0,1 ]$; not a function 
C) 
  
D) 
 
 $[ - 8,8 ] ; [ 0,8 ] ;$ not a function
$[ - 8,8 ] ; [ - 1,0 ]$; function

Question 20

Provide an appropriate response.
-If the vertex of the graph of a quadratic function lies in quadrant I and the graph is concave down, how many $\mathrm { x }$-intercepts does the graph have?

Accepted Answer

A)  2 
B)  0 
C)  1 
D)  3 
A)  2 
B)  0 
C)  1 
D)  3

Give the focus, directrix, and axis for the parabola. - $( y - 6 ) ^ { 2 } = - 12 ( x + 2 )$

Identify the type of graph. - $x ^ { 2 } - 9 x + y = 0$

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $4 y=\sqrt{3 x^{2}-12}$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - 4 y=\sqrt{3 x^{2}-12}$

Graph the parabola. - $x = ( y + 5 ) ^ { 2 } + 6$ $Graph the parabola. - x = ( y + 5 ) ^ { 2 } + 6$

Provide an appropriate response. - $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1 \text { are } ( 2,0 ) \text { and } ( - 2,0 )$ The x-intercepts of the hyperbola with equation

Write an equation for the ellipse. - $\mathrm { x }$ -intercepts $( \pm 6,0 ) ; \mathrm { y }$ -intercepts $( 0 , \pm 3 )$

Write an equation for the parabola with vertex at the origin. -Focus $\left( - \frac { 1 } { 7 } , 0 \right)$

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether a parabola opens up or down or whether it opens left or right.

Write an equation for the hyperbola. - $x$ -intercepts $( \pm 5,0 )$ ; center at origin; passing through $( 5 \sqrt { 5 } , 6 )$

Graph the conic section. - $25 ( x - 5 ) ^ { 2 } + 16 ( y - 2 ) ^ { 2 } = 400$ $Graph the conic section. - 25 ( x - 5 ) ^ { 2 } + 16 ( y - 2 ) ^ { 2 } = 400$

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 sum of the distances from the points (4, 0) and (-4, 0) is 28.

Provide an appropriate response. - $Provide an appropriate response. - Using only this graph of f ( x ) = a ( x - h ) ^ { 2 } + k , what are the signs of h and k ?$ Using only this graph of $f ( x ) = a ( x - h ) ^ { 2 } + k$ , what are the signs of $h$ and $k$ ?

Match the equation of the ellipse with the appropriate description. - $16 x ^ { 2 } + 49 y ^ { 2 } = 3136$

Provide an appropriate response. -An ellipse has eccentricity between 0 and 1. 114)

Find the eccentricity e of the hyperbola. - $x ^ { 2 } - 2 y ^ { 2 } = 6$

Find the eccentricity e of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 49$

Write an equation for the parabola with vertex at the origin. -Focus $( 0,7 )$

Write an equation for the ellipse. -foci at $( - 6 , - 3 ) , ( 0 , - 3 )$ ; major axis length of 10

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $y = - \sqrt { 1 - \frac { x ^ { 2 } } { 64 } }$ $Graph the equation. Give the domain and range. Identify whether the equation is a function. - y = - \sqrt { 1 - \frac { x ^ { 2 } } { 64 } }$

Provide an appropriate response. -If the vertex of the graph of a quadratic function lies in quadrant I and the graph is concave down, how many $\mathrm { x }$ -intercepts does the graph have?

Review of Basic Concepts

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

Filters

Exam 11: Analytic Geometry

Give the focus, directrix, and axis for the parabola. - (y−6)2=−12(x+2)( y - 6 ) ^ { 2 } = - 12 ( x + 2 )(y−6)2=−12(x+2)

Identify the type of graph. - x2−9x+y=0x ^ { 2 } - 9 x + y = 0x2−9x+y=0

Graph the equation. Give the domain and range. Identify whether the equation is a function. - 4y=3x2−124 y=\sqrt{3 x^{2}-12}4y=3x2−12​

Graph the parabola. - x=(y+5)2+6x = ( y + 5 ) ^ { 2 } + 6x=(y+5)2+6

Provide an appropriate response. - x236−y24=1 are (2,0) and (−2,0)\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1 \text { are } ( 2,0 ) \text { and } ( - 2,0 )36x2​−4y2​=1 are (2,0) and (−2,0) The x-intercepts of the hyperbola with equation

Write an equation for the ellipse. - x\mathrm { x }x -intercepts (±6,0);y( \pm 6,0 ) ; \mathrm { y }(±6,0);y -intercepts (0,±3)( 0 , \pm 3 )(0,±3)

Write an equation for the parabola with vertex at the origin. -Focus (−17,0)\left( - \frac { 1 } { 7 } , 0 \right)(−71​,0)