Question 1

Graph the parabola.
-$$x = y ^ { 2 } - 4$$

Accepted Answer

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

Question 2

Write an equation for the ellipse.
-foci at $( \pm 2 \sqrt { 15 } , 0 ) ; x$-intercepts $\pm 8$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 8 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 2 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 8 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 2 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 3

Write an equation for the hyperbola.
-vertices at $( 3,0 ) , ( - 3,0 )$; foci at $( 9,0 ) , ( - 9,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 72 } = 1$ 
D)  $\frac { x ^ { 2 } } { 72 } - \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 72 } = 1$ 
D)  $\frac { x ^ { 2 } } { 72 } - \frac { y ^ { 2 } } { 9 } = 1$

Question 4

Graph the conic section.
-$$x ^ { 2 } - 4 y - 4 x = 0$$

Accepted Answer

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

Question 5

Graph the ellipse.
-$$\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$$
 
 xx

Accepted Answer

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

Question 6

Write the word or phrase that best completes each statement or answers the question.
-Suppose that $A = 0$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$. What kind of graph does this equation have?

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

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

Accepted Answer

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

Question 8

Write an equation for the parabola with vertex at the origin.
-Through $( 4,3 )$, opening to the right

Accepted Answer

A)  $y ^ { 2 } = \frac { 9 } { 4 } x$ 
B)  $y ^ { 2 } = - \frac { 9 } { 4 } x$ 
C)  $x ^ { 2 } = \frac { 16 } { 3 } y$ 
D)  $x = \frac { 9 } { 4 } y ^ { 2 }$ 
A)  $y ^ { 2 } = \frac { 9 } { 4 } x$ 
B)  $y ^ { 2 } = - \frac { 9 } { 4 } x$ 
C)  $x ^ { 2 } = \frac { 16 } { 3 } y$ 
D)  $x = \frac { 9 } { 4 } y ^ { 2 }$

Question 9

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 36 } = 1$ 
A)  $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 36 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 36 } = 1$

Question 10

Write an equation for the ellipse.
-foci at $( 0,11 ) , ( 0 , - 11 )$, through the point $\left( 1 , \frac { 61 \sqrt { 3599 } } { 60 } \right)$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 3721 } + \frac { y ^ { 2 } } { 3600 } = 1$ 
B)  $\frac { x ^ { 2 } } { 60 } + \frac { y ^ { 2 } } { 61 } = 1$ 
C)  $\frac { x ^ { 2 } } { 3600 } + \frac { y ^ { 2 } } { 3721 } = 1$ 
D)  $\frac { x ^ { 2 } } { 61 } + \frac { y ^ { 2 } } { 60 } = 1$ 
A)  $\frac { x ^ { 2 } } { 3721 } + \frac { y ^ { 2 } } { 3600 } = 1$ 
B)  $\frac { x ^ { 2 } } { 60 } + \frac { y ^ { 2 } } { 61 } = 1$ 
C)  $\frac { x ^ { 2 } } { 3600 } + \frac { y ^ { 2 } } { 3721 } = 1$ 
D)  $\frac { x ^ { 2 } } { 61 } + \frac { y ^ { 2 } } { 60 } = 1$

Question 11

Graph the conic section.
-

Accepted Answer

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

Question 12

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

Accepted Answer

A)  $( 0,7 ) , y = - 7 , y$-axis 
B)  $( 7,0 ) , x = - 7 , x$-axis 
C)  $( 7,7 ) , x = 7 , x$-axis 
D)  $( 7,0 ) , x = - 7 , y$-axis 
A)  $( 0,7 ) , y = - 7 , y$-axis 
B)  $( 7,0 ) , x = - 7 , x$-axis 
C)  $( 7,7 ) , x = 7 , x$-axis 
D)  $( 7,0 ) , x = - 7 , y$-axis

Question 13

Write an equation for the parabola.
-vertex: $( - 2,5 )$, directrix: $y = 11$

Accepted Answer

A)  $( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$ 
B)  $( y + 2 ) ^ { 2 } = 8 ( x - 5 )$ 
C)  $( y + 2 ) ^ { 2 } = - 24 ( x - 5 )$ 
D)  $( x + 2 ) ^ { 2 } = - 24 ( y + 5 )$ 
A)  $( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$ 
B)  $( y + 2 ) ^ { 2 } = 8 ( x - 5 )$ 
C)  $( y + 2 ) ^ { 2 } = - 24 ( x - 5 )$ 
D)  $( x + 2 ) ^ { 2 } = - 24 ( y + 5 )$

Question 14

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

Accepted Answer

A)  $( - 6,0 ) , x = 6 , x$-axis 
B)  $( 0 , - 6 ) , y = 6 , y$-axis 
C)  $( - 6,0 ) , y = 6 , y$-axis 
D)  $( 6,0 ) , x = - 6 , x$-axis 
A)  $( - 6,0 ) , x = 6 , x$-axis 
B)  $( 0 , - 6 ) , y = 6 , y$-axis 
C)  $( - 6,0 ) , y = 6 , y$-axis 
D)  $( 6,0 ) , x = - 6 , x$-axis

Question 15

Graph the conic section.
-

Accepted Answer

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

Question 16

Write the word or phrase that best completes each statement or answers the question.
-Discuss the symmetries exhibited by an ellipse centered at the origin.

Accepted Answer

An ellipse centered at the ori

Question 17

Graph the ellipse.
-$16 x^{2}+49 y^{2}=784$

Accepted Answer

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

Question 18

Write an equation for the ellipse.
-foci at $( - 5 , - 2 ) , ( 1 , - 2 )$; major axis length of 10

Accepted Answer

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

Question 19

Write the word or phrase that best completes each statement or answers the question.
-A student thinks that the graphs of the equations $$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1 \text { and } \frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 1$$ are identical. Is the student correct? Explain.

Accepted Answer

No, the student is incorrect. Although b

Question 20

Identify the type of graph.
-$$\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

A)  The graph is an ellipse with foci on the $x$-axis 
B)  The graph is a circle with center at $( 0,0 )$. 
C)  The graph is a circle with center at $( 64,64 )$. 
D)  The graph is a circle with center at $( 8,8 )$. 
A)  The graph is an ellipse with foci on the $x$-axis 
B)  The graph is a circle with center at $( 0,0 )$. 
C)  The graph is a circle with center at $( 64,64 )$. 
D)  The graph is a circle with center at $( 8,8 )$.

Graph the parabola. - $x = y ^ { 2 } - 4$ $Graph the parabola. - x = y ^ { 2 } - 4$

Write an equation for the ellipse. -foci at $( \pm 2 \sqrt { 15 } , 0 ) ; x$ -intercepts $\pm 8$

Write an equation for the hyperbola. -vertices at $( 3,0 ) , ( - 3,0 )$ ; foci at $( 9,0 ) , ( - 9,0 )$

Graph the conic section. - $x ^ { 2 } - 4 y - 4 x = 0$ $Graph the conic section. - x ^ { 2 } - 4 y - 4 x = 0$

Graph the ellipse. - $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ $Graph the ellipse. - \frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1 xx$ xx

Write the word or phrase that best completes each statement or answers the question. -Suppose that $A = 0$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$ . What kind of graph does this equation have?

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

Write an equation for the parabola with vertex at the origin. -Through $( 4,3 )$ , opening to the right

Choose the equation that matches the graph. -

Write an equation for the ellipse. -foci at $( 0,11 ) , ( 0 , - 11 )$ , through the point $\left( 1 , \frac { 61 \sqrt { 3599 } } { 60 } \right)$

Graph the conic section. -

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

Write an equation for the parabola. -vertex: $( - 2,5 )$ , directrix: $y = 11$

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

Graph the conic section. -

Write the word or phrase that best completes each statement or answers the question. -Discuss the symmetries exhibited by an ellipse centered at the origin.

Graph the ellipse. - $16 x^{2}+49 y^{2}=784$ $Graph the ellipse. - 16 x^{2}+49 y^{2}=784$

Write an equation for the ellipse. -foci at $( - 5 , - 2 ) , ( 1 , - 2 )$ ; major axis length of 10

Identify the type of graph. - $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

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=y2−4x = y ^ { 2 } - 4x=y2−4

Write an equation for the ellipse. -foci at (±215,0);x( \pm 2 \sqrt { 15 } , 0 ) ; x(±215​,0);x -intercepts ±8\pm 8±8

Write an equation for the hyperbola. -vertices at (3,0),(−3,0)( 3,0 ) , ( - 3,0 )(3,0),(−3,0) ; foci at (9,0),(−9,0)( 9,0 ) , ( - 9,0 )(9,0),(−9,0)

Graph the conic section. - x2−4y−4x=0x ^ { 2 } - 4 y - 4 x = 0x2−4y−4x=0

Graph the ellipse. - (x−2)216+(y−1)24=1\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 116(x−2)2​+4(y−1)2​=1 xx

Write the word or phrase that best completes each statement or answers the question. -Suppose that A=0A = 0A=0 in the equation Ax2+Bx+Cy2+Dy+E=0A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0Ax2+Bx+Cy2+Dy+E=0 . What kind of graph does this equation have?

Match the equation of the parabola with the appropriate description. - y=6+2x−x2y = 6 + 2 x - x ^ { 2 }y=6+2x−x2

Write an equation for the parabola with vertex at the origin. -Through (4,3)( 4,3 )(4,3) , opening to the right

Choose the equation that matches the graph. -

Write an equation for the ellipse. -foci at (0,11),(0,−11)( 0,11 ) , ( 0 , - 11 )(0,11),(0,−11) , through the point (1,61359960)\left( 1 , \frac { 61 \sqrt { 3599 } } { 60 } \right)(1,60613599​​)

Graph the conic section. -

Give the focus, directrix, and axis for the parabola. - y2=28xy ^ { 2 } = 28 xy2=28x

Write an equation for the parabola. -vertex: (−2,5)( - 2,5 )(−2,5) , directrix: y=11y = 11y=11

Give the focus, directrix, and axis for the parabola. - y2=−24xy ^ { 2 } = - 24 xy2=−24x

Graph the conic section. -

Write the word or phrase that best completes each statement or answers the question. -Discuss the symmetries exhibited by an ellipse centered at the origin.

Graph the ellipse. - 16x2+49y2=78416 x^{2}+49 y^{2}=78416x2+49y2=784

Write an equation for the ellipse. -foci at (−5,−2),(1,−2)( - 5 , - 2 ) , ( 1 , - 2 )(−5,−2),(1,−2) ; major axis length of 10

Identify the type of graph. - x264+y264=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 164x2​+64y2​=1

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. - $x = y ^ { 2 } - 4$ $Graph the parabola. - x = y ^ { 2 } - 4$

Write an equation for the ellipse. -foci at $( \pm 2 \sqrt { 15 } , 0 ) ; x$ -intercepts $\pm 8$

Write an equation for the hyperbola. -vertices at $( 3,0 ) , ( - 3,0 )$ ; foci at $( 9,0 ) , ( - 9,0 )$

Graph the conic section. - $x ^ { 2 } - 4 y - 4 x = 0$ $Graph the conic section. - x ^ { 2 } - 4 y - 4 x = 0$

Graph the ellipse. - $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ $Graph the ellipse. - \frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1 xx$ xx

Write the word or phrase that best completes each statement or answers the question. -Suppose that $A = 0$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$ . What kind of graph does this equation have?

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

Write an equation for the parabola with vertex at the origin. -Through $( 4,3 )$ , opening to the right

Write an equation for the ellipse. -foci at $( 0,11 ) , ( 0 , - 11 )$ , through the point $\left( 1 , \frac { 61 \sqrt { 3599 } } { 60 } \right)$

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

Write an equation for the parabola. -vertex: $( - 2,5 )$ , directrix: $y = 11$

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

Graph the ellipse. - $16 x^{2}+49 y^{2}=784$ $Graph the ellipse. - 16 x^{2}+49 y^{2}=784$

Write an equation for the ellipse. -foci at $( - 5 , - 2 ) , ( 1 , - 2 )$ ; major axis length of 10

Identify the type of graph. - $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$