Question 1

Tech: Rotation of Axes
-$3 x^{2}-4 x y+3 y^{2}-2 x+5 y=10$

Accepted Answer

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

Question 2

Convert the equation to the standard form for an ellipse by completing the square on x and y.
-$$36 x ^ { 2 } + 16 y ^ { 2 } + 216 x - 64 y - 188 = 0$$

Accepted Answer

A)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ 
B)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { ( x + 3 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 36 } = 1$ 
A)  $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ 
B)  $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { ( x + 3 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 3 ) ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 36 } = 1$

Question 3

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection.
-$$\begin{array} { r } 
4 x ^ { 2 } + y ^ { 2 } = 4 \
y ^ { 2 } - 4 x ^ { 2 } = 4
\end{array}$$

Accepted Answer

A)  $\{ ( 0 , - 2 ) , ( 0,2 ) \}$ 
B)  $\{ ( 0 , - 2 ) \}$ 
C)  $\{ ( 0,4 ) \}$ 
D)  $\{ ( 2,0 ) , ( 2,0 ) \}$ 
A)  $\{ ( 0 , - 2 ) , ( 0,2 ) \}$ 
B)  $\{ ( 0 , - 2 ) \}$ 
C)  $\{ ( 0,4 ) \}$ 
D)  $\{ ( 2,0 ) , ( 2,0 ) \}$

Question 4

Write Equations of Rotated Conics in Standard Form
-$$x ^ { 2 } + 2 x y + y ^ { 2 } + x - y - 4 = 0$$

Accepted Answer

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

Question 5

Understand the Advantages of Parametric Representations
-A baseball pitcher throws a baseball with an initial velocity of 126 feet per second at an angle of $20 ^ { \circ }$ to the horizontal. The ball leaves the pitcher's hand at a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball?

Accepted Answer

A) 
$\begin{array}{l}
x=118.4 \mathrm{t} ; \mathrm{y}=-16 \mathrm{t}^{2}+43.09 \mathrm{t}+5 \
2.805 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
34.012 \text { feet }
\end{array}$ 
B) 
$\begin{array}{l}
x=118.4 t ; y=-16 t^{2}+43.09 t+5 \
5.609 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
29.012 \text { feet }
\end{array}$ 
C) 
$\begin{array}{l}
x=118.4 \mathrm{t} ; \mathrm{y}=-16 \mathrm{t}^{2}+43.09 \mathrm{t}+5 \
2.572 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
4.985 \text { feet }
\end{array}$ 
D) 
$\begin{array}{l}
x=118.4 t ; y=-16 t^{2}+43.09 t+5 \
5.143 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
237.094 \text { feet }
\end{array}$ 
A) 
$\begin{array}{l}
x=118.4 \mathrm{t} ; \mathrm{y}=-16 \mathrm{t}^{2}+43.09 \mathrm{t}+5 \
2.805 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
34.012 \text { feet }
\end{array}$ 
B) 
$\begin{array}{l}
x=118.4 t ; y=-16 t^{2}+43.09 t+5 \
5.609 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
29.012 \text { feet }
\end{array}$ 
C) 
$\begin{array}{l}
x=118.4 \mathrm{t} ; \mathrm{y}=-16 \mathrm{t}^{2}+43.09 \mathrm{t}+5 \
2.572 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
4.985 \text { feet }
\end{array}$ 
D) 
$\begin{array}{l}
x=118.4 t ; y=-16 t^{2}+43.09 t+5 \
5.143 \mathrm{sec} ; \
1.347 \mathrm{sec} ; \
237.094 \text { feet }
\end{array}$

Question 6

Graph Parabolas with Vertices Not at the Origin
-$$( y - 2 ) ^ { 2 } = 4 ( x - 3 )$$

Accepted Answer

A)  vertex: $( 3,2 )$
focus: $( 4,2 )$
directrix: $x = 2$ 
B)  vertex: $( - 3 , - 2 )$
focus: $( - 2 , - 2 )$
directrix: $x = - 4 \quad$ 
C)  vertex: $( 2,3 )$
focus: $( 3,3 )$
 directrix: $x = 1$ 
D)  vertex: $( 3,2 )$
focus: $( 2,2 )$
directrix: $x = 4$ 
A)  vertex: $( 3,2 )$
focus: $( 4,2 )$
directrix: $x = 2$ 
B)  vertex: $( - 3 , - 2 )$
focus: $( - 2 , - 2 )$
directrix: $x = - 4 \quad$ 
C)  vertex: $( 2,3 )$
focus: $( 3,3 )$
 directrix: $x = 1$ 
D)  vertex: $( 3,2 )$
focus: $( 2,2 )$
directrix: $x = 4$

Question 7

Graph Hyperbolas Not Centered at the Origin
-$$( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64$$

Accepted Answer

A)  Center: $( - 2,3 )$; Vertices: $( - 10,3 )$ and $( 6,3 )$; Foci: $( - 2 - \sqrt { 65 } , 3 )$ and $( - 2 + \sqrt { 65 } , 3 )$ 
B)  Center: $( 2 , - 3 )$; Vertices: $( - 6 , - 3 )$ and $( 10 , - 3 )$; Foci: $( 2 - \sqrt { 65 } , 3 )$ and $( 2 + \sqrt { 65 } , 3 )$ 
C)  Center: $( - 2,3 )$; Vertices: $( - 9,4 )$ and $( 7,4 )$; Foci: $( - 1 - \sqrt { 65 } , 4 )$ and $( - 1 + \sqrt { 65 } , 4 )$ 
D)  Center: $( - 2,3 )$; Vertices: $( 8,3 )$ and $( - 8,3 )$; Foci: $( - \sqrt { 65 } , 3 )$ and $( \sqrt { 65 } , 3 )$ 
A)  Center: $( - 2,3 )$; Vertices: $( - 10,3 )$ and $( 6,3 )$; Foci: $( - 2 - \sqrt { 65 } , 3 )$ and $( - 2 + \sqrt { 65 } , 3 )$ 
B)  Center: $( 2 , - 3 )$; Vertices: $( - 6 , - 3 )$ and $( 10 , - 3 )$; Foci: $( 2 - \sqrt { 65 } , 3 )$ and $( 2 + \sqrt { 65 } , 3 )$ 
C)  Center: $( - 2,3 )$; Vertices: $( - 9,4 )$ and $( 7,4 )$; Foci: $( - 1 - \sqrt { 65 } , 4 )$ and $( - 1 + \sqrt { 65 } , 4 )$ 
D)  Center: $( - 2,3 )$; Vertices: $( 8,3 )$ and $( - 8,3 )$; Foci: $( - \sqrt { 65 } , 3 )$ and $( \sqrt { 65 } , 3 )$

Question 8

Use the center, vertices, and asymptotes to graph the hyperbola.
-$$\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$$

Accepted Answer

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

Question 9

Graph the parabola.
-$$x ^ { 2 } = - 5 y$$

Accepted Answer

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

Question 10

Graph Hyperbolas Centered at the Origin
-$$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  Asymptotes: $y = \pm \frac { 2 } { 3 } x$
  
B)  Asymptotes: $y = \pm \frac { 3 } { 2 } x$
  
C)  Asymptotes: $y = \pm \frac { 2 } { 3 } x$
  
D)  Asymptotes: $y = \pm \frac { 3 } { 2 } x$
  
A)  Asymptotes: $y = \pm \frac { 2 } { 3 } x$
  
B)  Asymptotes: $y = \pm \frac { 3 } { 2 } x$
  
C)  Asymptotes: $y = \pm \frac { 2 } { 3 } x$
  
D)  Asymptotes: $y = \pm \frac { 3 } { 2 } x$

Question 11

Parametric Equations
1 Use Point Plotting to Graph Plane Curves Described by Parametric Equations
-$x = \left( 40 \cos 30 ^ { \circ } \right) t , y = 6 + \left( 40 \sin 30 ^ { \circ } \right) t - 10 t ^ { 2 } ; t = 6$

Accepted Answer

A)  $( 120 \sqrt { 3 } , - 234 )$ 
B)  $( 240 \sqrt { 3 } , 220 )$ 
C)  $( 120 \sqrt { 3 } , 66 )$ 
D)  $( - 120 \sqrt { 3 } , 172 )$ 
A)  $( 120 \sqrt { 3 } , - 234 )$ 
B)  $( 240 \sqrt { 3 } , 220 )$ 
C)  $( 120 \sqrt { 3 } , 66 )$ 
D)  $( - 120 \sqrt { 3 } , 172 )$

Question 12

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

Accepted Answer

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

Question 13

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 14

The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$x = 10 y ^ { 2 }$$

Accepted Answer

A)  focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = - \frac { 1 } { 40 }$ 
B)  focus: $\left( 0 , \frac { 1 } { 40 } \right)$
directrix: $y = - \frac { 1 } { 40 }$ 
C)  focus: $\left( \frac { 1 } { 10 } , 0 \right)$
 directrix: $x = - \frac { 1 } { 10 }$ 
D)  focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = \frac { 1 } { 40 }$ 
A)  focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = - \frac { 1 } { 40 }$ 
B)  focus: $\left( 0 , \frac { 1 } { 40 } \right)$
directrix: $y = - \frac { 1 } { 40 }$ 
C)  focus: $\left( \frac { 1 } { 10 } , 0 \right)$
 directrix: $x = - \frac { 1 } { 10 }$ 
D)  focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = \frac { 1 } { 40 }$

Question 15

Graph the ellipse and locate the foci.
-$$\frac { x ^ { 2 } } { \frac { 7 } { 4 } } + \frac { y ^ { 2 } } { \frac { 9 } { 4 } } = 1$$
Round to the nearest tenth if necessary.

Accepted Answer

A)  foci $( 0,0.7 )$ and $( 0 , - 0.7 )$
  
B)  foci $( 0.7,0 )$ and $( 0 , - 0.7 )$
  
C)  foci $( 0,0.7 )$ and $( 0 , - 0.7 )$
  
D)  foci $( 0.8,0 )$ and $( 0 , - 0.8 )$
  
A)  foci $( 0,0.7 )$ and $( 0 , - 0.7 )$
  
B)  foci $( 0.7,0 )$ and $( 0 , - 0.7 )$
  
C)  foci $( 0,0.7 )$ and $( 0 , - 0.7 )$
  
D)  foci $( 0.8,0 )$ and $( 0 , - 0.8 )$

Question 16

Identify Conics Without Rotating Axes
-$$x ^ { 2 } - 9 x y + 3 y ^ { 2 } - 14 = 0$$

Accepted Answer

A)  hyperbola 
B)  parabola 
C)  ellipse 
D)  circle 
A)  hyperbola 
B)  parabola 
C)  ellipse 
D)  circle

Question 17

Find Parametric Equations for Functions
-Circle: Center: $( 2,3 )$; Radius: 2

Accepted Answer

A)  $x = 2 + 2 \cos t ; y = 3 + 2 \sin t$ 
B)  $x = t - 2 ; ( y - 3 ) ^ { 2 } + t ^ { 2 } = 4$ 
C)  $x = 3 + 2 \sin \mathrm { t } ; \mathrm { y } = 2 + 2 \cos \mathrm { t }$ 
D)  $x = 2 + \sin t ; y = 3 + \cos t$ 
A)  $x = 2 + 2 \cos t ; y = 3 + 2 \sin t$ 
B)  $x = t - 2 ; ( y - 3 ) ^ { 2 } + t ^ { 2 } = 4$ 
C)  $x = 3 + 2 \sin \mathrm { t } ; \mathrm { y } = 2 + 2 \cos \mathrm { t }$ 
D)  $x = 2 + \sin t ; y = 3 + \cos t$

Question 18

Graph Hyperbolas Not Centered at the Origin
-$\frac { ( y - 4 ) ^ { 2 } } { 49 } - \frac { ( x - 4 ) ^ { 2 } } { 9 } = 1$

Accepted Answer

A)  Center: $( 4,4 )$; Vertices: $( 4 , - 3 )$ and $( 4,11 )$; Foci: $( 4,4 - \sqrt { 58 } )$ and $( 4,4 + \sqrt { 58 } )$ 
B)  Center: $( - 4 , - 4 )$; Vertices: $( - 4 , - 11 )$ and $( - 4,3 )$; Foci: $( - 4 , - 4 - \sqrt { 58 } )$ and $( - 4 , - 4 + \sqrt { 58 } )$ 
C)  Center: $( 4,4 )$; Vertices: $( 4,4 - \sqrt { 58 } )$ and $( 4,4 + \sqrt { 58 } )$; Foci: $( 4 , - 3 )$ and $( 4,11 )$ 
D)  Center: $( 4,4 )$; Vertices: $( 3 , - 2 )$ and $( 5,12 )$; Foci: $( 3,5 - \sqrt { 58 } )$ and $( 5,5 + \sqrt { 58 } )$ 
A)  Center: $( 4,4 )$; Vertices: $( 4 , - 3 )$ and $( 4,11 )$; Foci: $( 4,4 - \sqrt { 58 } )$ and $( 4,4 + \sqrt { 58 } )$ 
B)  Center: $( - 4 , - 4 )$; Vertices: $( - 4 , - 11 )$ and $( - 4,3 )$; Foci: $( - 4 , - 4 - \sqrt { 58 } )$ and $( - 4 , - 4 + \sqrt { 58 } )$ 
C)  Center: $( 4,4 )$; Vertices: $( 4,4 - \sqrt { 58 } )$ and $( 4,4 + \sqrt { 58 } )$; Foci: $( 4 , - 3 )$ and $( 4,11 )$ 
D)  Center: $( 4,4 )$; Vertices: $( 3 , - 2 )$ and $( 5,12 )$; Foci: $( 3,5 - \sqrt { 58 } )$ and $( 5,5 + \sqrt { 58 } )$

Question 19

Use the center, vertices, and asymptotes to graph the hyperbola.
-$(x+2)^{2}-4(y-1)^{2}=4$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Question 20

Graph Parabolas with Vertices Not at the Origin
-$( \mathrm { x } - 1 ) ^ { 2 } = - 12 ( \mathrm { y } + 2 )$

Accepted Answer

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

Tech: Rotation of Axes - $3 x^{2}-4 x y+3 y^{2}-2 x+5 y=10$ $Tech: Rotation of Axes - 3 x^{2}-4 x y+3 y^{2}-2 x+5 y=10$

Convert the equation to the standard form for an ellipse by completing the square on x and y. - $36 x ^ { 2 } + 16 y ^ { 2 } + 216 x - 64 y - 188 = 0$

Write Equations of Rotated Conics in Standard Form - $x ^ { 2 } + 2 x y + y ^ { 2 } + x - y - 4 = 0$

Graph Parabolas with Vertices Not at the Origin - $( y - 2 ) ^ { 2 } = 4 ( x - 3 )$

Graph Hyperbolas Not Centered at the Origin - $( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64$

Use the center, vertices, and asymptotes to graph the hyperbola. - $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ $Use the center, vertices, and asymptotes to graph the hyperbola. - \frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$

Graph the parabola. - $x ^ { 2 } = - 5 y$ $Graph the parabola. - x ^ { 2 } = - 5 y$

Graph Hyperbolas Centered at the Origin - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$ $Graph Hyperbolas Centered at the Origin - \frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$

Parametric Equations 1 Use Point Plotting to Graph Plane Curves Described by Parametric Equations - $x = \left( 40 \cos 30 ^ { \circ } \right) t , y = 6 + \left( 40 \sin 30 ^ { \circ } \right) t - 10 t ^ { 2 } ; t = 6$

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

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

The Parabola 1 Graph Parabolas with Vertices at the Origin - $x = 10 y ^ { 2 }$

Identify Conics Without Rotating Axes - $x ^ { 2 } - 9 x y + 3 y ^ { 2 } - 14 = 0$

Find Parametric Equations for Functions -Circle: Center: $( 2,3 )$ ; Radius: 2

Graph Hyperbolas Not Centered at the Origin - $\frac { ( y - 4 ) ^ { 2 } } { 49 } - \frac { ( x - 4 ) ^ { 2 } } { 9 } = 1$

Use the center, vertices, and asymptotes to graph the hyperbola. - $(x+2)^{2}-4(y-1)^{2}=4$ $Use the center, vertices, and asymptotes to graph the hyperbola. - (x+2)^{2}-4(y-1)^{2}=4$

Graph Parabolas with Vertices Not at the Origin - $( \mathrm { x } - 1 ) ^ { 2 } = - 12 ( \mathrm { y } + 2 )$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 10: Conic Sections and Analytic Geometry

Tech: Rotation of Axes - 3x2−4xy+3y2−2x+5y=103 x^{2}-4 x y+3 y^{2}-2 x+5 y=103x2−4xy+3y2−2x+5y=10

Convert the equation to the standard form for an ellipse by completing the square on x and y. - 36x2+16y2+216x−64y−188=036 x ^ { 2 } + 16 y ^ { 2 } + 216 x - 64 y - 188 = 036x2+16y2+216x−64y−188=0

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. - 4+=4 -4=4

Write Equations of Rotated Conics in Standard Form - x2+2xy+y2+x−y−4=0x ^ { 2 } + 2 x y + y ^ { 2 } + x - y - 4 = 0x2+2xy+y2+x−y−4=0

Graph Parabolas with Vertices Not at the Origin - (y−2)2=4(x−3)( y - 2 ) ^ { 2 } = 4 ( x - 3 )(y−2)2=4(x−3)

Graph Hyperbolas Not Centered at the Origin - (x+2)2−64(y−3)2=64( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64(x+2)2−64(y−3)2=64

Use the center, vertices, and asymptotes to graph the hyperbola. - (x−2)24−(y+2)225=1\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 14(x−2)2​−25(y+2)2​=1

Graph the parabola. - x2=−5yx ^ { 2 } = - 5 yx2=−5y

Graph Hyperbolas Centered at the Origin - y24−x29=1\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 14y2​−9x2​=1

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

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

The Parabola 1 Graph Parabolas with Vertices at the Origin - x=10y2x = 10 y ^ { 2 }x=10y2

Graph the ellipse and locate the foci. - x274+y294=1\frac { x ^ { 2 } } { \frac { 7 } { 4 } } + \frac { y ^ { 2 } } { \frac { 9 } { 4 } } = 147​x2​+49​y2​=1 Round to the nearest tenth if necessary.

Identify Conics Without Rotating Axes - x2−9xy+3y2−14=0x ^ { 2 } - 9 x y + 3 y ^ { 2 } - 14 = 0x2−9xy+3y2−14=0

Find Parametric Equations for Functions -Circle: Center: (2,3)( 2,3 )(2,3) ; Radius: 2

Graph Hyperbolas Not Centered at the Origin - (y−4)249−(x−4)29=1\frac { ( y - 4 ) ^ { 2 } } { 49 } - \frac { ( x - 4 ) ^ { 2 } } { 9 } = 149(y−4)2​−9(x−4)2​=1

Use the center, vertices, and asymptotes to graph the hyperbola. - (x+2)2−4(y−1)2=4(x+2)^{2}-4(y-1)^{2}=4(x+2)2−4(y−1)2=4

Graph Parabolas with Vertices Not at the Origin - (x−1)2=−12(y+2)( \mathrm { x } - 1 ) ^ { 2 } = - 12 ( \mathrm { y } + 2 )(x−1)2=−12(y+2)

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Tech: Rotation of Axes - $3 x^{2}-4 x y+3 y^{2}-2 x+5 y=10$ $Tech: Rotation of Axes - 3 x^{2}-4 x y+3 y^{2}-2 x+5 y=10$

Convert the equation to the standard form for an ellipse by completing the square on x and y. - $36 x ^ { 2 } + 16 y ^ { 2 } + 216 x - 64 y - 188 = 0$

Write Equations of Rotated Conics in Standard Form - $x ^ { 2 } + 2 x y + y ^ { 2 } + x - y - 4 = 0$

Graph Parabolas with Vertices Not at the Origin - $( y - 2 ) ^ { 2 } = 4 ( x - 3 )$

Graph Hyperbolas Not Centered at the Origin - $( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64$

Use the center, vertices, and asymptotes to graph the hyperbola. - $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ $Use the center, vertices, and asymptotes to graph the hyperbola. - \frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$

Graph the parabola. - $x ^ { 2 } = - 5 y$ $Graph the parabola. - x ^ { 2 } = - 5 y$

Graph Hyperbolas Centered at the Origin - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$ $Graph Hyperbolas Centered at the Origin - \frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$

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

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

The Parabola 1 Graph Parabolas with Vertices at the Origin - $x = 10 y ^ { 2 }$

Identify Conics Without Rotating Axes - $x ^ { 2 } - 9 x y + 3 y ^ { 2 } - 14 = 0$

Find Parametric Equations for Functions -Circle: Center: $( 2,3 )$ ; Radius: 2

Graph Hyperbolas Not Centered at the Origin - $\frac { ( y - 4 ) ^ { 2 } } { 49 } - \frac { ( x - 4 ) ^ { 2 } } { 9 } = 1$

Use the center, vertices, and asymptotes to graph the hyperbola. - $(x+2)^{2}-4(y-1)^{2}=4$ $Use the center, vertices, and asymptotes to graph the hyperbola. - (x+2)^{2}-4(y-1)^{2}=4$

Graph Parabolas with Vertices Not at the Origin - $( \mathrm { x } - 1 ) ^ { 2 } = - 12 ( \mathrm { y } + 2 )$