Question 1

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

Accepted Answer

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

Question 2

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. At some point along the road from the
Lowest point of the cable, the cable is 1.96 inches above the roadway. Find the distance between that point and
The base of the nearest tower.

Accepted Answer

A)  21 in. 
B)  13.8 in. 
C)  14.2 in. 
D)  21.2 in. 
A)  21 in. 
B)  13.8 in. 
C)  14.2 in. 
D)  21.2 in.

Question 3

Identify the equation without completing the square.
-$$y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$$

Accepted Answer

A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  not a conic 
A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  not a conic

Question 4

Solve the problem.
-A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

Accepted Answer

A)  0.1 in. from the vertex 
B)  10.1 in. from the vertex 
C)  0.2 in. from the vertex 
D)  0.8 in. from the vertex 
A)  0.1 in. from the vertex 
B)  10.1 in. from the vertex 
C)  0.2 in. from the vertex 
D)  0.8 in. from the vertex

Question 5

Graph the curve whose parametric equations are given.
-$x=2 t, y=t+5 ;-2 \leq t \leq 3$

Accepted Answer

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

Question 6

Find the center, foci, and vertices of the ellipse.
-$$\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  center at $( 1 , - 2 )$
foci at $( 1 + 3 \sqrt { 3 } , 1 ) , ( 1 - 3 \sqrt { 3 } , 1 )$
vertices at $( 6 , - 2 ) , ( - 6 , - 2 )$ 
B)  center at $( - 2,1 )$
foci at $( - 2 + 3 \sqrt { 3 } , 1 ) , ( - 2 - 3 \sqrt { 3 } , 1 )$
vertices at $( - 5 , - 2 ) , ( 7 , - 2 )$ 
C)  center at $( 1 , - 2 )$
foci at $( - 3 \sqrt { 3 } , - 2 ) , ( 3 \sqrt { 3 } , - 2 )$
vertices at $( 6 , - 2 ) , ( - 6 , - 2 )$ 
D)  center at $( 1 , - 2 )$
foci at $( 1 + 3 \sqrt { 3 } , - 2 ) , ( 1 - 3 \sqrt { 3 } , - 2 )$
vertices at $( - 5 , - 2 ) , ( 7 , - 2 )$ 
A)  center at $( 1 , - 2 )$
foci at $( 1 + 3 \sqrt { 3 } , 1 ) , ( 1 - 3 \sqrt { 3 } , 1 )$
vertices at $( 6 , - 2 ) , ( - 6 , - 2 )$ 
B)  center at $( - 2,1 )$
foci at $( - 2 + 3 \sqrt { 3 } , 1 ) , ( - 2 - 3 \sqrt { 3 } , 1 )$
vertices at $( - 5 , - 2 ) , ( 7 , - 2 )$ 
C)  center at $( 1 , - 2 )$
foci at $( - 3 \sqrt { 3 } , - 2 ) , ( 3 \sqrt { 3 } , - 2 )$
vertices at $( 6 , - 2 ) , ( - 6 , - 2 )$ 
D)  center at $( 1 , - 2 )$
foci at $( 1 + 3 \sqrt { 3 } , - 2 ) , ( 1 - 3 \sqrt { 3 } , - 2 )$
vertices at $( - 5 , - 2 ) , ( 7 , - 2 )$

Question 7

Graph the hyperbola.
-$25 x^{2}=9 y^{2}+225$

Accepted Answer

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

Question 8

Find an equation for the ellipse described. Graph the equation.
-Foci at $( - 4 , - 1 )$ and $( 2 , - 1 )$; length of major axis is 10

Accepted Answer

A)

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

$\frac { ( x - 2 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1$ 
A)

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

$\frac { ( x - 2 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1$

Question 9

Convert the polar equation to a rectangular equation.
-$$r = \frac { 2 } { 2 - 2 \cos \theta }$$

Accepted Answer

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

Question 10

Graph the hyperbola.
-$25 y^{2}=9 x^{2}+225$

Accepted Answer

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

Question 11

Solve the problem.
-A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 30 feet from the center is to be 6 feet. Find the height of the arch at its center.

Accepted Answer

A)  30.25 ft 
B)  7.79 ft 
C)  6.33 ft 
D)  9.4 ft 
A)  30.25 ft 
B)  7.79 ft 
C)  6.33 ft 
D)  9.4 ft

Question 12

Find an equation for the parabola described.
-Vertex at (3, -4); focus at (3, -6) A) $( x - 3 ) ^ { 2 } = 8 ( y + 4 )$

Accepted Answer

B)  $( x - 3 ) ^ { 2 } = - 8 ( y + 4 )$ 
C)  $( y - 4 ) ^ { 2 } = - 12 ( x + 3 )$ 
D)  $( y - 4 ) ^ { 2 } = 12 ( x + 3 )$ 
B)  $( x - 3 ) ^ { 2 } = - 8 ( y + 4 )$ 
C)  $( y - 4 ) ^ { 2 } = - 12 ( x + 3 )$ 
D)  $( y - 4 ) ^ { 2 } = 12 ( x + 3 )$

Question 13

Graph the curve whose parametric equations are given.
-$x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$

Accepted Answer

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

Question 14

Identify the equation without applying a rotation of axes.
-$$3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$$

Accepted Answer

A)  parabola 
B)  hyperbola 
C)  ellipse 
D)  not a conic 
A)  parabola 
B)  hyperbola 
C)  ellipse 
D)  not a conic

Question 15

Graph the ellipse and locate the foci.
-$\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$

Accepted Answer

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

Question 16

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 5 \cos t , y = - 2 \sin t ; 0 \leq t \leq 2 \pi$$

Accepted Answer

A)  $4 x ^ { 2 } + 25 y ^ { 2 } = 100 ; - 5 \leq x \leq 5$ 
B)  $4 x ^ { 2 } - 25 y ^ { 2 } = 100 ; x \geq 5$ 
C)  $4 x ^ { 2 } + 25 y ^ { 2 } = 1 ; - \frac { 1 } { 5 } \leq x \leq \frac { 1 } { 5 }$ 
D)  $4 x ^ { 2 } - 25 y ^ { 2 } = 1 ; x \geq \frac { 1 } { 2 }$ 
A)  $4 x ^ { 2 } + 25 y ^ { 2 } = 100 ; - 5 \leq x \leq 5$ 
B)  $4 x ^ { 2 } - 25 y ^ { 2 } = 100 ; x \geq 5$ 
C)  $4 x ^ { 2 } + 25 y ^ { 2 } = 1 ; - \frac { 1 } { 5 } \leq x \leq \frac { 1 } { 5 }$ 
D)  $4 x ^ { 2 } - 25 y ^ { 2 } = 1 ; x \geq \frac { 1 } { 2 }$

Question 17

Solve the problem.
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Accepted Answer

A)  3.6 ft 
B)  21.8 ft 
C)  0.2 ft 
D)  29.1 ft 
A)  3.6 ft 
B)  21.8 ft 
C)  0.2 ft 
D)  29.1 ft

Question 18

Graph the ellipse and locate the foci.
-$4 x^{2}+16 y^{2}=64$

Accepted Answer

A)  foci at $( 5,0 )$ and $( - 5,0 )$
  
B)  foci at $( \sqrt { 7 } , 0 )$ and $( - \sqrt { 7 } , 0 )$
  
C)  foci at $( 4,0 )$ and $( - 4,0 )$
  
D)  foci at $( 0 , \sqrt { 7 } )$ and $( 0 , - \sqrt { 7 } )$
  
A)  foci at $( 5,0 )$ and $( - 5,0 )$
  
B)  foci at $( \sqrt { 7 } , 0 )$ and $( - \sqrt { 7 } , 0 )$
  
C)  foci at $( 4,0 )$ and $( - 4,0 )$
  
D)  foci at $( 0 , \sqrt { 7 } )$ and $( 0 , - \sqrt { 7 } )$

Question 19

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 8 feet across, how deep should the searchlight be?

Accepted Answer

A)  4 ft 
B)  0.8 ft 
C)  1.6 ft 
D)  3.2 ft 
A)  4 ft 
B)  0.8 ft 
C)  1.6 ft 
D)  3.2 ft

Question 20

Graph the curve whose parametric equations are given.
-$$\begin{array} { l } 
C _ { 1 } : x = 7 \sin t , y = 7 - 7 \cos ^ { 2 } t ; \frac { \pi } { 2 } \leq t \leq \frac { 3 \pi } { 2 } \
C _ { 2 } : x = \ln t , y = \ln t ^ { 2 } ; e ^ { - 4 } \leq t \leq e ^ { 3 } \
C _ { 3 } : x = t ^ { 2 } - 8 , y = t - 3 ; - 4 \leq t \leq 4 \
C _ { 4 } : x = t - 5 , y = t + 2 ; - 4 \leq t \leq 7
\end{array}$$

Accepted Answer

The answer of Graph the curve whose parametric equations are...

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

Identify the equation without completing the square. - $y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$

Solve the problem. -A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

Graph the curve whose parametric equations are given. - $x=2 t, y=t+5 ;-2 \leq t \leq 3$ $Graph the curve whose parametric equations are given. - x=2 t, y=t+5 ;-2 \leq t \leq 3$

Find the center, foci, and vertices of the ellipse. - $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$

Graph the hyperbola. - $25 x^{2}=9 y^{2}+225$ $Graph the hyperbola. - 25 x^{2}=9 y^{2}+225$

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 4 , - 1 )$ and $( 2 , - 1 )$ ; length of major axis is 10

Convert the polar equation to a rectangular equation. - $r = \frac { 2 } { 2 - 2 \cos \theta }$

Graph the hyperbola. - $25 y^{2}=9 x^{2}+225$ $Graph the hyperbola. - 25 y^{2}=9 x^{2}+225$

Solve the problem. -A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 30 feet from the center is to be 6 feet. Find the height of the arch at its center.

Find an equation for the parabola described. -Vertex at (3, -4); focus at (3, -6) A) $( x - 3 ) ^ { 2 } = 8 ( y + 4 )$ B) $( x - 3 ) ^ { 2 } = - 8 ( y + 4 )$ C) $( y - 4 ) ^ { 2 } = - 12 ( x + 3 )$ D) $( y - 4 ) ^ { 2 } = 12 ( x + 3 )$

Graph the curve whose parametric equations are given. - $x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$ $Graph the curve whose parametric equations are given. - x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$

Identify the equation without applying a rotation of axes. - $3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$

Graph the ellipse and locate the foci. - $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$ $Graph the ellipse and locate the foci. - \frac{x^{2}}{9}+\frac{y^{2}}{16}=1$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 5 \cos t , y = - 2 \sin t ; 0 \leq t \leq 2 \pi$

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Graph the ellipse and locate the foci. - $4 x^{2}+16 y^{2}=64$ $Graph the ellipse and locate the foci. - 4 x^{2}+16 y^{2}=64$

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 8 feet across, how deep should the searchlight be?

Graph the curve whose parametric equations are given. - :x=7t,y=7-7t;\leqt\leq :x=t,y=;\leqt\leq :x=-8,y=t-3;-4\leqt\leq4 :x=t-5,y=t+2;-4\leqt\leq7

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 9: Analytic Geometry

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

Identify the equation without completing the square. - y2−4x2+8x+4y+3=0y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0y2−4x2+8x+4y+3=0

Solve the problem. -A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

Graph the curve whose parametric equations are given. - x=2t,y=t+5;−2≤t≤3x=2 t, y=t+5 ;-2 \leq t \leq 3x=2t,y=t+5;−2≤t≤3

Find the center, foci, and vertices of the ellipse. - (x−1)236+(y+2)29=1\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 136(x−1)2​+9(y+2)2​=1

Graph the hyperbola. - 25x2=9y2+22525 x^{2}=9 y^{2}+22525x2=9y2+225

Find an equation for the ellipse described. Graph the equation. -Foci at (−4,−1)( - 4 , - 1 )(−4,−1) and (2,−1)( 2 , - 1 )(2,−1) ; length of major axis is 10

Convert the polar equation to a rectangular equation. - r=22−2cos⁡θr = \frac { 2 } { 2 - 2 \cos \theta }r=2−2cosθ2​

Graph the hyperbola. - 25y2=9x2+22525 y^{2}=9 x^{2}+22525y2=9x2+225

Solve the problem. -A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 30 feet from the center is to be 6 feet. Find the height of the arch at its center.

Graph the curve whose parametric equations are given. - x=t3+1,y=t3−10;−2≤t≤2x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2x=t3+1,y=t3−10;−2≤t≤2

Identify the equation without applying a rotation of axes. - 3x2+8xy+2y2+3x+2y+10=03 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 03x2+8xy+2y2+3x+2y+10=0

Graph the ellipse and locate the foci. - x29+y216=1\frac{x^{2}}{9}+\frac{y^{2}}{16}=19x2​+16y2​=1

Find a rectangular equation for the plane curve defined by the parametric equations. - x=5cos⁡t,y=−2sin⁡t;0≤t≤2πx = 5 \cos t , y = - 2 \sin t ; 0 \leq t \leq 2 \pix=5cost,y=−2sint;0≤t≤2π

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Graph the ellipse and locate the foci. - 4x2+16y2=644 x^{2}+16 y^{2}=644x2+16y2=64

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 8 feet across, how deep should the searchlight be?

Graph the curve whose parametric equations are given. - :x=7t,y=7-7t;\leqt\leq :x=t,y=;\leqt\leq :x=-8,y=t-3;-4\leqt\leq4 :x=t-5,y=t+2;-4\leqt\leq7

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

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

Identify the equation without completing the square. - $y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$

Graph the curve whose parametric equations are given. - $x=2 t, y=t+5 ;-2 \leq t \leq 3$ $Graph the curve whose parametric equations are given. - x=2 t, y=t+5 ;-2 \leq t \leq 3$

Find the center, foci, and vertices of the ellipse. - $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$

Graph the hyperbola. - $25 x^{2}=9 y^{2}+225$ $Graph the hyperbola. - 25 x^{2}=9 y^{2}+225$

Find an equation for the ellipse described. Graph the equation. -Foci at $( - 4 , - 1 )$ and $( 2 , - 1 )$ ; length of major axis is 10

Convert the polar equation to a rectangular equation. - $r = \frac { 2 } { 2 - 2 \cos \theta }$

Graph the hyperbola. - $25 y^{2}=9 x^{2}+225$ $Graph the hyperbola. - 25 y^{2}=9 x^{2}+225$

Graph the curve whose parametric equations are given. - $x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$ $Graph the curve whose parametric equations are given. - x=t^{3}+1, y=t^{3}-10 ;-2 \leq t \leq 2$

Identify the equation without applying a rotation of axes. - $3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$

Graph the ellipse and locate the foci. - $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$ $Graph the ellipse and locate the foci. - \frac{x^{2}}{9}+\frac{y^{2}}{16}=1$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 5 \cos t , y = - 2 \sin t ; 0 \leq t \leq 2 \pi$

Graph the ellipse and locate the foci. - $4 x^{2}+16 y^{2}=64$ $Graph the ellipse and locate the foci. - 4 x^{2}+16 y^{2}=64$