Question 1

Match the equation to the graph.
-$$( y + 2 ) ^ { 2 } = 8 ( x + 1 )$$

Accepted Answer

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

Question 2

Find an equation for the ellipse described. Graph the equation.
-Foci at (1, 3) and (-5, 3); vertex at (-9, 3)

Accepted Answer

A)  $\frac { ( x + 2 ) ^ { 2 } } { 49 } + \frac { ( y - 3 ) ^ { 2 } } { 40 } = 1$
  
B)  $\frac { ( x - 3 ) ^ { 2 } } { 49 } + \frac { ( y + 2 ) ^ { 2 } } { 40 } = 1$
  
C)  $\frac { ( x + 2 ) ^ { 2 } } { 40 } + \frac { ( y - 3 ) ^ { 2 } } { 49 } = 1$
  
D)  $\frac { ( x - 3 ) ^ { 2 } } { 40 } + \frac { ( y + 2 ) ^ { 2 } } { 49 } = 1$
  
A)  $\frac { ( x + 2 ) ^ { 2 } } { 49 } + \frac { ( y - 3 ) ^ { 2 } } { 40 } = 1$
  
B)  $\frac { ( x - 3 ) ^ { 2 } } { 49 } + \frac { ( y + 2 ) ^ { 2 } } { 40 } = 1$
  
C)  $\frac { ( x + 2 ) ^ { 2 } } { 40 } + \frac { ( y - 3 ) ^ { 2 } } { 49 } = 1$
  
D)  $\frac { ( x - 3 ) ^ { 2 } } { 40 } + \frac { ( y + 2 ) ^ { 2 } } { 49 } = 1$

Question 3

Match the equation to the graph.
-$$( y - 1 ) ^ { 2 } = - 7 ( x + 1 )$$

Accepted Answer

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

Question 4

Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second
Tower. The towers are both 12.25 inches tall and stand 70 inches apart. Find the vertical distance from the
Roadway to the cable at a point on the road 14 inches from the lowest point of the cable.

Accepted Answer

A)  1.76 in. 
B)  7.84 in. 
C)  2.16 in. 
D)  1.96 in. 
A)  1.76 in. 
B)  7.84 in. 
C)  2.16 in. 
D)  1.96 in.

Question 5

Graph the equation.
-$$( y - 1 ) ^ { 2 } = - 5 ( x - 1 )$$

Accepted Answer

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

Question 6

Find the vertex, focus, and directrix of the parabola.
-$$x ^ { 2 } = - 12 y$$

Accepted Answer

A)  vertex: $( 0,0 )$
focus: $( 3,0 )$
directrix: $y = -3$
  
B)  vertex: $( 0,0 )$
focus: $( 0,-3 )$
directrix: $y = 3$
  
C)  vertex: $( 0,0 )$
focus: $( 0,3 )$
directrix: $y = - 3$
  
D)  vertex: $( 0,0 )$
focus: $( - 3,0 )$
directrix: $x = 3$
  
A)  vertex: $( 0,0 )$
focus: $( 3,0 )$
directrix: $y = -3$
  
B)  vertex: $( 0,0 )$
focus: $( 0,-3 )$
directrix: $y = 3$
  
C)  vertex: $( 0,0 )$
focus: $( 0,3 )$
directrix: $y = - 3$
  
D)  vertex: $( 0,0 )$
focus: $( - 3,0 )$
directrix: $x = 3$

Question 7

Graph the ellipse and locate the foci.
-$$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$$

Accepted Answer

A)  foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$
  
B)  foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$
  
C)  foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$
  
D)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
A)  foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$
  
B)  foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$
  
C)  foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$
  
D)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

Question 8

Match the equation to the graph.
-

Accepted Answer

A)  vertex: $( 5,3 )$
focus: $( 8,3 )$
directrix: $x = 2$
  
B)  vertex: $( 5,3 )$
focus: $( 5,6 )$
directrix: $\mathrm { y } = 0$
  
C)  vertex: $( 5,3 )$
focus: $( 2,3 )$
directrix: $x = 8$
  
D)  vertex: $( 5,3 )$
focus: $( 5,0 )$
directrix: $y = 6$
  
A)  vertex: $( 5,3 )$
focus: $( 8,3 )$
directrix: $x = 2$
  
B)  vertex: $( 5,3 )$
focus: $( 5,6 )$
directrix: $\mathrm { y } = 0$
  
C)  vertex: $( 5,3 )$
focus: $( 2,3 )$
directrix: $x = 8$
  
D)  vertex: $( 5,3 )$
focus: $( 5,0 )$
directrix: $y = 6$

Question 9

Match the equation to the graph.
-

Accepted Answer

A)  vertex: $( - 4 , - 4 )$
focus: $( - 4 , - 7 )$
directrix: $\mathrm { y } = - 1$
  
B)  vertex: $( - 4 , - 4 )$
focus: $( - 4 , - 1 )$
directrix: $y = - 7$
  
C)  vertex: $( - 4 , - 4 )$
focus: $( - 7 , - 4 )$
directrix: $x = - 1$
  
D)  vertex: $( - 4 , - 4 )$
focus: $( - 1 , - 4 )$
directrix: $x = - 7$
  
A)  vertex: $( - 4 , - 4 )$
focus: $( - 4 , - 7 )$
directrix: $\mathrm { y } = - 1$
  
B)  vertex: $( - 4 , - 4 )$
focus: $( - 4 , - 1 )$
directrix: $y = - 7$
  
C)  vertex: $( - 4 , - 4 )$
focus: $( - 7 , - 4 )$
directrix: $x = - 1$
  
D)  vertex: $( - 4 , - 4 )$
focus: $( - 1 , - 4 )$
directrix: $x = - 7$

Question 10

Solve the problem.
-A hall 130 feet in length was designed as a whispering gallery. If the ceiling is 25 feet high at the center, how far
from the center are the foci located?

Accepted Answer

The answer of Solve the problem.
-A hall 130 feet in...

Question 11

Graph the equation.
-$y^{2}=-12 x$

Accepted Answer

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

Question 12

Write an equation for the graph.
-

Accepted Answer

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

Question 13

Find an equation for the ellipse described.
-Vertices at (-2, 4) and (12, 4); focus at (10, 4)

Accepted Answer

A)  $\frac { ( x - 4 ) ^ { 2 } } { 36 } + \frac { ( y - 5 ) ^ { 2 } } { 23 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 81 } - \frac { ( y + 4 ) ^ { 2 } } { 29 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 49 } + \frac { ( y - 4 ) ^ { 2 } } { 24 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 25 } + \frac { ( y + 4 ) ^ { 2 } } { 24 } = 1$ 
A)  $\frac { ( x - 4 ) ^ { 2 } } { 36 } + \frac { ( y - 5 ) ^ { 2 } } { 23 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 81 } - \frac { ( y + 4 ) ^ { 2 } } { 29 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 49 } + \frac { ( y - 4 ) ^ { 2 } } { 24 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 25 } + \frac { ( y + 4 ) ^ { 2 } } { 24 } = 1$

Question 14

Name the conic.
-$$x ^ { 2 } = 9 y$$

Accepted Answer

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

Question 15

Match the equation to the graph.
-$$\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$$

Accepted Answer

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

Question 16

Solve the problem.
-A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 14 feet across, how deep should the searchlight be?

Accepted Answer

A)  12.3 ft 
B)  2.5 ft 
C)  9.8 ft 
D)  0.9 ft 
A)  12.3 ft 
B)  2.5 ft 
C)  9.8 ft 
D)  0.9 ft

Question 17

Solve the problem.
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 142 feet and a maximum height of 25 feet. Find the height of the arch at 25 feet from its center.

Accepted Answer

A)  21.9 ft 
B)  0.8 ft 
C)  71 ft 
D)  12.4 ft 
A)  21.9 ft 
B)  0.8 ft 
C)  71 ft 
D)  12.4 ft

Question 18

Solve the problem.
-A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 30 feet and the distance across the top of the mirror is 50 inches, how deep is the mirror in the center?

Accepted Answer

A)  9 in. 
B)  $\frac { 125 } { 288 } \mathrm { in }$. 
C)  $\frac { 125 } { 3456 }$ in. 
D)  $\frac { 125 } { 24 } \mathrm { in } .$ 
A)  9 in. 
B)  $\frac { 125 } { 288 } \mathrm { in }$. 
C)  $\frac { 125 } { 3456 }$ in. 
D)  $\frac { 125 } { 24 } \mathrm { in } .$

Question 19

Find an equation for the ellipse described. Graph the equation.
-Vertices at (5, -4) and (5, 8); length of minor axis is 6

Accepted Answer

A) 
 
$\frac { ( x + 5 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$ 
B) 
 
$$\frac { ( x - 5 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$ 
C) 
 
$$\frac { ( x - 5 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$ 
D) 
 
$$\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$$ 
A) 
 
$\frac { ( x + 5 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$ 
B) 
 
$$\frac { ( x - 5 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$ 
C) 
 
$$\frac { ( x - 5 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$ 
D) 
 
$$\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$$

Question 20

Graph the equation.
-$$( x - 2 ) ^ { 2 } = 8 ( y + 1 )$$

Accepted Answer

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

Match the equation to the graph. - $( y + 2 ) ^ { 2 } = 8 ( x + 1 )$

Find an equation for the ellipse described. Graph the equation. -Foci at (1, 3) and (-5, 3); vertex at (-9, 3)

Match the equation to the graph. - $( y - 1 ) ^ { 2 } = - 7 ( x + 1 )$

Graph the equation. - $( y - 1 ) ^ { 2 } = - 5 ( x - 1 )$ $Graph the equation. - ( y - 1 ) ^ { 2 } = - 5 ( x - 1 )$

Find the vertex, focus, and directrix of the parabola. - $x ^ { 2 } = - 12 y$ $Find the vertex, focus, and directrix of the parabola. - x ^ { 2 } = - 12 y$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Match the equation to the graph. -

Match the equation to the graph. -

Solve the problem. -A hall 130 feet in length was designed as a whispering gallery. If the ceiling is 25 feet high at the center, how far from the center are the foci located?

Graph the equation. - $y^{2}=-12 x$ $Graph the equation. - y^{2}=-12 x$

Write an equation for the graph. -

Find an equation for the ellipse described. -Vertices at (-2, 4) and (12, 4); focus at (10, 4)

Name the conic. - $x ^ { 2 } = 9 y$

Match the equation to the graph. - $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$

Solve the problem. -A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 14 feet across, how deep should the searchlight be?

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 142 feet and a maximum height of 25 feet. Find the height of the arch at 25 feet from its center.

Solve the problem. -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 30 feet and the distance across the top of the mirror is 50 inches, how deep is the mirror in the center?

Find an equation for the ellipse described. Graph the equation. -Vertices at (5, -4) and (5, 8); length of minor axis is 6

Graph the equation. - $( x - 2 ) ^ { 2 } = 8 ( y + 1 )$ $Graph the equation. - ( x - 2 ) ^ { 2 } = 8 ( y + 1 )$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 5: Conics

Match the equation to the graph. - (y+2)2=8(x+1)( y + 2 ) ^ { 2 } = 8 ( x + 1 )(y+2)2=8(x+1)

Find an equation for the ellipse described. Graph the equation. -Foci at (1, 3) and (-5, 3); vertex at (-9, 3)

Match the equation to the graph. - (y−1)2=−7(x+1)( y - 1 ) ^ { 2 } = - 7 ( x + 1 )(y−1)2=−7(x+1)

Graph the equation. - (y−1)2=−5(x−1)( y - 1 ) ^ { 2 } = - 5 ( x - 1 )(y−1)2=−5(x−1)

Find the vertex, focus, and directrix of the parabola. - x2=−12yx ^ { 2 } = - 12 yx2=−12y

Graph the ellipse and locate the foci. - x29+y24=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 19x2​+4y2​=1

Match the equation to the graph. -

Match the equation to the graph. -

Solve the problem. -A hall 130 feet in length was designed as a whispering gallery. If the ceiling is 25 feet high at the center, how far from the center are the foci located?

Graph the equation. - y2=−12xy^{2}=-12 xy2=−12x

Write an equation for the graph. -

Find an equation for the ellipse described. -Vertices at (-2, 4) and (12, 4); focus at (10, 4)

Name the conic. - x2=9yx ^ { 2 } = 9 yx2=9y

Match the equation to the graph. - x29−y216=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 19x2​−16y2​=1

Solve the problem. -A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 14 feet across, how deep should the searchlight be?

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 142 feet and a maximum height of 25 feet. Find the height of the arch at 25 feet from its center.

Solve the problem. -A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 30 feet and the distance across the top of the mirror is 50 inches, how deep is the mirror in the center?

Find an equation for the ellipse described. Graph the equation. -Vertices at (5, -4) and (5, 8); length of minor axis is 6

Graph the equation. - (x−2)2=8(y+1)( x - 2 ) ^ { 2 } = 8 ( y + 1 )(x−2)2=8(y+1)

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Match the equation to the graph. - $( y + 2 ) ^ { 2 } = 8 ( x + 1 )$

Match the equation to the graph. - $( y - 1 ) ^ { 2 } = - 7 ( x + 1 )$

Graph the equation. - $( y - 1 ) ^ { 2 } = - 5 ( x - 1 )$ $Graph the equation. - ( y - 1 ) ^ { 2 } = - 5 ( x - 1 )$

Find the vertex, focus, and directrix of the parabola. - $x ^ { 2 } = - 12 y$ $Find the vertex, focus, and directrix of the parabola. - x ^ { 2 } = - 12 y$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Graph the equation. - $y^{2}=-12 x$ $Graph the equation. - y^{2}=-12 x$

Name the conic. - $x ^ { 2 } = 9 y$

Match the equation to the graph. - $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$

Graph the equation. - $( x - 2 ) ^ { 2 } = 8 ( y + 1 )$ $Graph the equation. - ( x - 2 ) ^ { 2 } = 8 ( y + 1 )$