Question 1

Find the eccentricity of the conic section shown in the graph.
-$$x = - 21$$

Accepted Answer

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

Question 2

Solve the problem.
-The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 27$, where $x$ and $y$ are in meters. Determine the distance, w, between the outside walls.
$\mathrm { A } = 11 \mathrm {~m}$

Accepted Answer

A)  $19.4 \mathrm {~m}$ 
B)  $94 \mathrm {~m}$ 
C)  $12.2 \mathrm {~m}$ 
D)  $9.7 \mathrm {~m}$ 
A)  $19.4 \mathrm {~m}$ 
B)  $94 \mathrm {~m}$ 
C)  $12.2 \mathrm {~m}$ 
D)  $9.7 \mathrm {~m}$

Question 3

The orbit of Mars around the sun is an ellipse with equation $$\frac { x ^ { 2 } } { 6241 } + \frac { y ^ { 2 } } { 5184 } = 1$$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Accepted Answer

A)  0.831 
B)  1.204 
C)  13.380 
D)  0.412 
A)  0.831 
B)  1.204 
C)  13.380 
D)  0.412

Question 4

Match the equation of the parabola with the appropriate description.
-$$y + 6 = 2 ( x + 10 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( 10 , - 6 )$ 
B)  Vertex at $( - 10 , - 6 )$ 
C)  Vertex at $( - 6,10 )$ 
D)  Vertex at $( 6,10 )$ 
A)  Vertex at $( 10 , - 6 )$ 
B)  Vertex at $( - 10 , - 6 )$ 
C)  Vertex at $( - 6,10 )$ 
D)  Vertex at $( 6,10 )$

Question 5

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$$x = 3 y ^ { 2 } + 3$$

Accepted Answer

A)  $y = \frac { \sqrt { x - 3 } } { \sqrt { 3 } }$ and $y = - \frac { \sqrt { x - 3 } } { \sqrt { 3 } }$ 
B)  $y = \sqrt { \frac { x } { 3 } - 3 }$ and $y = - \sqrt { \frac { x } { 3 } - 3 }$ 
C)  $y = \frac { \sqrt { x - 3 } } { 3 }$ and $y = - \frac { \sqrt { x - 3 } } { 3 }$ 
D)  $y = \frac { \sqrt { x - 3 } } { \sqrt { 3 } }$ and $y = \frac { \sqrt { 3 - x } } { \sqrt { 3 } }$ 
A)  $y = \frac { \sqrt { x - 3 } } { \sqrt { 3 } }$ and $y = - \frac { \sqrt { x - 3 } } { \sqrt { 3 } }$ 
B)  $y = \sqrt { \frac { x } { 3 } - 3 }$ and $y = - \sqrt { \frac { x } { 3 } - 3 }$ 
C)  $y = \frac { \sqrt { x - 3 } } { 3 }$ and $y = - \frac { \sqrt { x - 3 } } { 3 }$ 
D)  $y = \frac { \sqrt { x - 3 } } { \sqrt { 3 } }$ and $y = \frac { \sqrt { 3 - x } } { \sqrt { 3 } }$

Question 6

If the vertex of the graph of a quadratic function lies in quadrant I and the graph is concave up, how many $x$-intercepts does the graph have?

Accepted Answer

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

Question 7

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$x ^ { 2 } - y ^ { 2 } = 16$

Accepted Answer

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

Question 8

Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = - 0.1 ( \mathrm { x } - 4 ) ^ { 2 }$ is a parabola with ــــــــــ$x$-intercept(s). Its vertex is theــــــــــــــ point of the graph and has coordinatesـــــــــــــــــــ

Accepted Answer

A)  no; maximum (or highest); $( - 0.1,4 )$ 
B)  two; maximum (or highest); $( 4,0 )$ 
C)  one; minimum (or lowest); $( 4,0 )$ 
D)  one; maximum (or highest); $( 4,0 )$ 
A)  no; maximum (or highest); $( - 0.1,4 )$ 
B)  two; maximum (or highest); $( 4,0 )$ 
C)  one; minimum (or lowest); $( 4,0 )$ 
D)  one; maximum (or highest); $( 4,0 )$

Question 9

Give the focus, directrix, and axis for the parabola.
-$$( x + 1 ) ^ { 2 } = 12 ( y - 2 )$$

Accepted Answer

A)  $( 2,2 ) , y = - 4 , x = 2$ 
B)  $( - 1,5 ) , y = - 1 , x = - 1$ 
C)  $( - 1 , - 1 ) , x = 5 , y = 2$ 
D)  $( 1,1 ) , y = - 5 , x = 1$ 
A)  $( 2,2 ) , y = - 4 , x = 2$ 
B)  $( - 1,5 ) , y = - 1 , x = - 1$ 
C)  $( - 1 , - 1 ) , x = 5 , y = 2$ 
D)  $( 1,1 ) , y = - 5 , x = 1$

Question 10

Write an equation for the parabola.
-vertex $( 3,2 )$, focus $( 3,4 )$

Accepted Answer

A)  $( y - 2 ) ^ { 2 } = 8 ( x - 3 )$ 
B)  $2 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
C)  $8 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
D)  $y - 2 = 8 ( x - 3 ) ^ { 2 }$ 
A)  $( y - 2 ) ^ { 2 } = 8 ( x - 3 )$ 
B)  $2 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
C)  $8 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
D)  $y - 2 = 8 ( x - 3 ) ^ { 2 }$

Question 11

Graph the hyperbola.
-$$\frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x + 1 ) ^ { 2 } } { 64 } = 1$$

Accepted Answer

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

Question 12

Write an equation for the parabola with vertex at the origin.
-Focus $\left( \frac { 1 } { 5 } , 0 \right)$

Accepted Answer

A)  $x ^ { 2 } = 20 y$ 
B)  $y ^ { 2 } = \frac { 4 } { 5 } x$ 
C)  $x ^ { 2 } = \frac { 4 } { 5 } y$ 
D)  $y ^ { 2 } = 20 x$ 
A)  $x ^ { 2 } = 20 y$ 
B)  $y ^ { 2 } = \frac { 4 } { 5 } x$ 
C)  $x ^ { 2 } = \frac { 4 } { 5 } y$ 
D)  $y ^ { 2 } = 20 x$

Question 13

Solve the problem.
-A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 15 t ^ { 2 } + 540 t$. What is its maximum height?

Accepted Answer

A)  $7290 \mathrm { ft }$ 
B)  $4860 \mathrm { ft }$ 
C)  $2430 \mathrm { ft }$ 
D)  $3645 \mathrm { ft }$ 
A)  $7290 \mathrm { ft }$ 
B)  $4860 \mathrm { ft }$ 
C)  $2430 \mathrm { ft }$ 
D)  $3645 \mathrm { ft }$

Question 14

Write an equation for the parabola.
-vertex: $( - 3 , - 4 )$, directrix: $x = - 8$

Accepted Answer

A)  $( x + 4 ) ^ { 2 } = 20 ( y + 3 )$ 
B)  $( y + 4 ) ^ { 2 } = 20 ( x + 3 )$ 
C)  $( y + 4 ) ^ { 2 } = - 20 ( x + 3 )$ 
D)  $( x + 3 ) ^ { 2 } = - 20 ( x + 4 )$ 
A)  $( x + 4 ) ^ { 2 } = 20 ( y + 3 )$ 
B)  $( y + 4 ) ^ { 2 } = 20 ( x + 3 )$ 
C)  $( y + 4 ) ^ { 2 } = - 20 ( x + 3 )$ 
D)  $( x + 3 ) ^ { 2 } = - 20 ( x + 4 )$

Question 15

Write an equation for the hyperbola.
-vertices at $( 0 , \pm 10 )$, asymptotes at $y = \pm \frac { 5 } { 2 } x$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ 
B)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 4 } = 1$ 
C)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 16 } = 1$ 
A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ 
B)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 4 } = 1$ 
C)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 16 } = 1$

Question 16

Graph the hyperbola.
-$25 x^{2}-4 y^{2}=100$

Accepted Answer

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

Question 17

If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave up, how many $x$-intercepts does the graph have?

Accepted Answer

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

Question 18

Explain why the vertex of a parabola must lie on its axis.

Accepted Answer

Explanations will vary. One possibility:

Question 19

Determine the two equations necessary to graph the hyperbola with a graphing calculator.
-$$y ^ { 2 } - 16 x ^ { 2 } = 16$$

Accepted Answer

A)  $\mathrm { y } = 4 + \sqrt { \mathrm { x } ^ { 2 } }$ and $- \mathrm { y } = - 4 - \sqrt { \mathrm { x } ^ { 2 } }$ 
B)  $y = 4 x ^ { 2 } + 4$ and $y = - 4 x ^ { 2 } - 4$ 
C)  $y = 4 \sqrt { x ^ { 2 } + 1 }$ and $y = - 4 \sqrt { x ^ { 2 } + 1 }$ 
D)  $y = 4 + \sqrt { x ^ { 2 } }$ and $y = 4 - \sqrt { x ^ { 2 } }$ 
A)  $\mathrm { y } = 4 + \sqrt { \mathrm { x } ^ { 2 } }$ and $- \mathrm { y } = - 4 - \sqrt { \mathrm { x } ^ { 2 } }$ 
B)  $y = 4 x ^ { 2 } + 4$ and $y = - 4 x ^ { 2 } - 4$ 
C)  $y = 4 \sqrt { x ^ { 2 } + 1 }$ and $y = - 4 \sqrt { x ^ { 2 } + 1 }$ 
D)  $y = 4 + \sqrt { x ^ { 2 } }$ and $y = 4 - \sqrt { x ^ { 2 } }$

Question 20

Graph the parabola.
-$$x = \frac { 4 } { 9 } ( y - 1 ) ^ { 2 } - 4$$

Accepted Answer

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

Find the eccentricity of the conic section shown in the graph. - $x = - 21$

The orbit of Mars around the sun is an ellipse with equation $\frac { x ^ { 2 } } { 6241 } + \frac { y ^ { 2 } } { 5184 } = 1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Match the equation of the parabola with the appropriate description. - $y + 6 = 2 ( x + 10 ) ^ { 2 }$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 3 y ^ { 2 } + 3$

If the vertex of the graph of a quadratic function lies in quadrant I and the graph is concave up, how many $x$ -intercepts does the graph have?

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } - y ^ { 2 } = 16$

Give the focus, directrix, and axis for the parabola. - $( x + 1 ) ^ { 2 } = 12 ( y - 2 )$

Write an equation for the parabola. -vertex $( 3,2 )$ , focus $( 3,4 )$

Graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x + 1 ) ^ { 2 } } { 64 } = 1$ $Graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x + 1 ) ^ { 2 } } { 64 } = 1$

Write an equation for the parabola with vertex at the origin. -Focus $\left( \frac { 1 } { 5 } , 0 \right)$

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 15 t ^ { 2 } + 540 t$ . What is its maximum height?

Write an equation for the parabola. -vertex: $( - 3 , - 4 )$ , directrix: $x = - 8$

Write an equation for the hyperbola. -vertices at $( 0 , \pm 10 )$ , asymptotes at $y = \pm \frac { 5 } { 2 } x$

Graph the hyperbola. - $25 x^{2}-4 y^{2}=100$ $Graph the hyperbola. - 25 x^{2}-4 y^{2}=100$

If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave up, how many $x$ -intercepts does the graph have?

Explain why the vertex of a parabola must lie on its axis.

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - $y ^ { 2 } - 16 x ^ { 2 } = 16$

Graph the parabola. - $x = \frac { 4 } { 9 } ( y - 1 ) ^ { 2 } - 4$ $Graph the parabola. - x = \frac { 4 } { 9 } ( y - 1 ) ^ { 2 } - 4$

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

Find the eccentricity of the conic section shown in the graph. - x=−21x = - 21x=−21

Solve the problem. -The roof of a building is in the shape of the hyperbola y2−x2=27y ^ { 2 } - x ^ { 2 } = 27y2−x2=27 , where xxx and yyy are in meters. Determine the distance, w, between the outside walls. A=11 m\mathrm { A } = 11 \mathrm {~m}A=11 m

The orbit of Mars around the sun is an ellipse with equation x26241+y25184=1\frac { x ^ { 2 } } { 6241 } + \frac { y ^ { 2 } } { 5184 } = 16241x2​+5184y2​=1 where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Match the equation of the parabola with the appropriate description. - y+6=2(x+10)2y + 6 = 2 ( x + 10 ) ^ { 2 }y+6=2(x+10)2

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x=3y2+3x = 3 y ^ { 2 } + 3x=3y2+3

If the vertex of the graph of a quadratic function lies in quadrant I and the graph is concave up, how many xxx -intercepts does the graph have?

Identify the equation as a parabola, circle, ellipse, or hyperbola. - x2−y2=16x ^ { 2 } - y ^ { 2 } = 16x2−y2=16

Give the focus, directrix, and axis for the parabola. - (x+1)2=12(y−2)( x + 1 ) ^ { 2 } = 12 ( y - 2 )(x+1)2=12(y−2)

Write an equation for the parabola. -vertex (3,2)( 3,2 )(3,2) , focus (3,4)( 3,4 )(3,4)

Graph the hyperbola. - (y+2)225−(x+1)264=1\frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x + 1 ) ^ { 2 } } { 64 } = 125(y+2)2​−64(x+1)2​=1

Write an equation for the parabola with vertex at the origin. -Focus (15,0)\left( \frac { 1 } { 5 } , 0 \right)(51​,0)

Solve the problem. -A projectile is thrown upward so that its distance above the ground after ttt seconds is h=−15t2+540th = - 15 t ^ { 2 } + 540 th=−15t2+540t . What is its maximum height?

Write an equation for the parabola. -vertex: (−3,−4)( - 3 , - 4 )(−3,−4) , directrix: x=−8x = - 8x=−8

Write an equation for the hyperbola. -vertices at (0,±10)( 0 , \pm 10 )(0,±10) , asymptotes at y=±52xy = \pm \frac { 5 } { 2 } xy=±25​x

Graph the hyperbola. - 25x2−4y2=10025 x^{2}-4 y^{2}=10025x2−4y2=100

If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave up, how many xxx -intercepts does the graph have?

Explain why the vertex of a parabola must lie on its axis.

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - y2−16x2=16y ^ { 2 } - 16 x ^ { 2 } = 16y2−16x2=16

Graph the parabola. - x=49(y−1)2−4x = \frac { 4 } { 9 } ( y - 1 ) ^ { 2 } - 4x=94​(y−1)2−4

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

Find the eccentricity of the conic section shown in the graph. - $x = - 21$

The orbit of Mars around the sun is an ellipse with equation $\frac { x ^ { 2 } } { 6241 } + \frac { y ^ { 2 } } { 5184 } = 1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Match the equation of the parabola with the appropriate description. - $y + 6 = 2 ( x + 10 ) ^ { 2 }$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 3 y ^ { 2 } + 3$

If the vertex of the graph of a quadratic function lies in quadrant I and the graph is concave up, how many $x$ -intercepts does the graph have?

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } - y ^ { 2 } = 16$

Give the focus, directrix, and axis for the parabola. - $( x + 1 ) ^ { 2 } = 12 ( y - 2 )$

Write an equation for the parabola. -vertex $( 3,2 )$ , focus $( 3,4 )$

Graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x + 1 ) ^ { 2 } } { 64 } = 1$ $Graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x + 1 ) ^ { 2 } } { 64 } = 1$

Write an equation for the parabola with vertex at the origin. -Focus $\left( \frac { 1 } { 5 } , 0 \right)$

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 15 t ^ { 2 } + 540 t$ . What is its maximum height?

Write an equation for the parabola. -vertex: $( - 3 , - 4 )$ , directrix: $x = - 8$

Write an equation for the hyperbola. -vertices at $( 0 , \pm 10 )$ , asymptotes at $y = \pm \frac { 5 } { 2 } x$

Graph the hyperbola. - $25 x^{2}-4 y^{2}=100$ $Graph the hyperbola. - 25 x^{2}-4 y^{2}=100$

If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave up, how many $x$ -intercepts does the graph have?

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - $y ^ { 2 } - 16 x ^ { 2 } = 16$

Graph the parabola. - $x = \frac { 4 } { 9 } ( y - 1 ) ^ { 2 } - 4$ $Graph the parabola. - x = \frac { 4 } { 9 } ( y - 1 ) ^ { 2 } - 4$