Question 1

Solve.
-The sum of the squares of two numbers is 89. The sum of the two numbers is -13. Find the two numbers.

Accepted Answer

A)  $- 5$ and $8 ; - 8$ and 5 
B)  $- 8$ and $- 5$ 
C)  $- 8$ and $- 5 ; 5$ and 8 
D)  5 and 8 
A)  $- 5$ and $8 ; - 8$ and 5 
B)  $- 8$ and $- 5$ 
C)  $- 8$ and $- 5 ; 5$ and 8 
D)  5 and 8

Question 2

Graph the system.
-$\left\{\begin{aligned}
3 x+5 y & \geq 15 \
y & \geq x^{2}+1
\end{aligned}\right.$

Accepted Answer

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

Question 3

Sketch the graph of the equation.
-$x^{2}+y^{2}-8 y=0$

Accepted Answer

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

Question 4

Write an equation of the circle with the given center and radius.
-the origin; $\sqrt { 13 }$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 169$ 
B)  $x ^ { 2 } + y ^ { 2 } = \sqrt { 13 }$ 
C)  $x ^ { 2 } + y ^ { 2 } = 13$ 
D)  $x ^ { 2 } + y ^ { 2 } = \frac { 13 } { 4 }$ 
A)  $x ^ { 2 } + y ^ { 2 } = 169$ 
B)  $x ^ { 2 } + y ^ { 2 } = \sqrt { 13 }$ 
C)  $x ^ { 2 } + y ^ { 2 } = 13$ 
D)  $x ^ { 2 } + y ^ { 2 } = \frac { 13 } { 4 }$

Question 5

Graph the inequality.
-$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } \leq 1$

Accepted Answer

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

Question 6

Graph the inequality.
-$\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } \geq 1$

Accepted Answer

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

Question 7

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the
right. Do not graph.
-$y = - 5 x ^ { 2 } - 4 x + 2$

Accepted Answer

A)  upward 
B)  to the left 
C)  downward 
D)  to the right 
A)  upward 
B)  to the left 
C)  downward 
D)  to the right

Question 8

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.
-$x=y^{2}+10 y+26$

Accepted Answer

A)  vertex $( 1,5 )$
  
B)  vertex $( 1 , - 5 )$
  
C)  vertex $( - 1 , - 5 )$
  
D)  vertex $( - 5,1 )$
  
A)  vertex $( 1,5 )$
  
B)  vertex $( 1 , - 5 )$
  
C)  vertex $( - 1 , - 5 )$
  
D)  vertex $( - 5,1 )$

Question 9

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola.
-$16 x ^ { 2 } + 25 y ^ { 2 } = 400$

Accepted Answer

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

Question 10

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph.
-$\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 16 } = 1$

Accepted Answer

A)  hyperbola 
B)  ellipse 
A)  hyperbola 
B)  ellipse

Question 11

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { r } 
x ^ { 2 } + y ^ { 2 } = 65 \
4 x + 7 y = 0
\end{array} \right.$

Accepted Answer

A)  $( 7 , - 4 )$ 
B)  $( 7 , - 4 ) , ( - 7 , - 4 )$ 
C)  $( 7 , - 4 ) , ( - 7,4 )$ 
D)  $( 7,4 ) , ( - 7 , - 4 )$ 
A)  $( 7 , - 4 )$ 
B)  $( 7 , - 4 ) , ( - 7 , - 4 )$ 
C)  $( 7 , - 4 ) , ( - 7,4 )$ 
D)  $( 7,4 ) , ( - 7 , - 4 )$

Question 12

Sketch the graph of the equation.
-$y^{2}-x^{2}=36$

Accepted Answer

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

Question 13

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{aligned}
x ^ { 2 } + y ^ { 2 } & = 25 \
x & = y ^ { 2 } - 5
\end{aligned} \right.$

Accepted Answer

A)  $\varnothing$ 
B)  $( - 5,0 ) , ( 4,9 ) , ( 4 , - 9 )$ 
C)  $( 4,3 ) , ( 4 , - 3 )$ 
D)  $( - 5,0 ) , ( 4,3 ) , ( 4 , - 3 )$ 
A)  $\varnothing$ 
B)  $( - 5,0 ) , ( 4,9 ) , ( 4 , - 9 )$ 
C)  $( 4,3 ) , ( 4 , - 3 )$ 
D)  $( - 5,0 ) , ( 4,3 ) , ( 4 , - 3 )$

Question 14

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { circle } & \text { ellipse } & \text { hyperbola } \
\text { conic sections } & \text { vertex } & \text { diameter } \
\text { center } & \text { radius } & \text { nonlinear system of equations }
\end{array}$$
-A(n)-------- is the set of points in a plane such that the absolute value of the difference of the distance from two fixed points is constant.

Accepted Answer

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

Question 15

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph.
-$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Accepted Answer

A)  hyperbola 
B)  ellipse 
A)  hyperbola 
B)  ellipse

Question 16

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.
-$x=-2(y-6)^{2}+1$

Accepted Answer

A)  vertex $( 1 , - 6 )$
  
B)  vertex $( 6,1 )$
  
C)  vertex $( 1,6 )$
  
D)  vertex $( 1,6 )$
  
A)  vertex $( 1 , - 6 )$
  
B)  vertex $( 6,1 )$
  
C)  vertex $( 1,6 )$
  
D)  vertex $( 1,6 )$

Question 17

Sketch the graph of the equation.
-$\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$

Accepted Answer

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

Question 18

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.
-$y=2(x-1)^{2}+3$

Accepted Answer

A)  vertex $( 1,3 )$
  
B)  vertex $( 3,1 )$
  
C)  vertex $( - 1,3 )$
  
D)  vertex $( - 3 , - 1 )$
  
A)  vertex $( 1,3 )$
  
B)  vertex $( 3,1 )$
  
C)  vertex $( - 1,3 )$
  
D)  vertex $( - 3 , - 1 )$

Question 19

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and
radius.
-$y=-3 x^{2}+24 x-47$

Accepted Answer

A)  vertex $( - 4,1 )$
  
B)  vertex $( - 4 , - 1 )$
  
C)  vertex $( 4,1 )$
  
D)  vertex $( 1,4 )$
  
A)  vertex $( - 4,1 )$
  
B)  vertex $( - 4 , - 1 )$
  
C)  vertex $( 4,1 )$
  
D)  vertex $( 1,4 )$

Question 20

Write an equation of the circle with the given center and radius.
-$( 4,8 ) ; \sqrt { 17 }$

Accepted Answer

A)  $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 289$ 
B)  $( x + 4 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 17$ 
C)  $( x - 4 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 17$ 
D)  $( x - 8 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 289$ 
A)  $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 289$ 
B)  $( x + 4 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 17$ 
C)  $( x - 4 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 17$ 
D)  $( x - 8 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 289$

Solve. -The sum of the squares of two numbers is 89. The sum of the two numbers is -13. Find the two numbers.

Graph the system. - $\left\{\begin{aligned}3 x+5 y & \geq 15 \\y & \geq x^{2}+1\end{aligned}\right.$ $Graph the system. - \left\{\begin{aligned} 3 x+5 y & \geq 15 \\ y & \geq x^{2}+1 \end{aligned}\right.$

Sketch the graph of the equation. - $x^{2}+y^{2}-8 y=0$ $Sketch the graph of the equation. - x^{2}+y^{2}-8 y=0$

Write an equation of the circle with the given center and radius. -the origin; $\sqrt { 13 }$

Graph the inequality. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } \leq 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } \leq 1$

Graph the inequality. - $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } \geq 1$ $Graph the inequality. - \frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } \geq 1$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = - 5 x ^ { 2 } - 4 x + 2$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $16 x ^ { 2 } + 25 y ^ { 2 } = 400$

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 16 } = 1$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 65 \\4 x + 7 y = 0\end{array} \right.$

Sketch the graph of the equation. - $y^{2}-x^{2}=36$ $Sketch the graph of the equation. - y^{2}-x^{2}=36$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 25 \\x & = y ^ { 2 } - 5\end{aligned} \right.$

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Sketch the graph of the equation. - $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ $Sketch the graph of the equation. - \frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$

Write an equation of the circle with the given center and radius. - $( 4,8 ) ; \sqrt { 17 }$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Sequences, Series, and the Binomial Theorem

Filters

Exam 13: Conic Sections

Solve. -The sum of the squares of two numbers is 89. The sum of the two numbers is -13. Find the two numbers.

Graph the system. - {3x+5y≥15y≥x2+1\left\{\begin{aligned}3 x+5 y & \geq 15 \\y & \geq x^{2}+1\end{aligned}\right.{3x+5yy​≥15≥x2+1​

Sketch the graph of the equation. - x2+y2−8y=0x^{2}+y^{2}-8 y=0x2+y2−8y=0

Write an equation of the circle with the given center and radius. -the origin; 13\sqrt { 13 }13​

Graph the inequality. - x216+y24≤1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } \leq 116x2​+4y2​≤1

Graph the inequality. - y216−x29≥1\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } \geq 116y2​−9x2​≥1

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - y=−5x2−4x+2y = - 5 x ^ { 2 } - 4 x + 2y=−5x2−4x+2

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x=y2+10y+26x=y^{2}+10 y+26x=y2+10y+26

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - 16x2+25y2=40016 x ^ { 2 } + 25 y ^ { 2 } = 40016x2+25y2=400

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - y225+x216=1\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 16 } = 125y2​+16x2​=1

Solve the nonlinear system of equations for real solutions. - {x2+y2=654x+7y=0\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 65 \\4 x + 7 y = 0\end{array} \right.{x2+y2=654x+7y=0​

Sketch the graph of the equation. - y2−x2=36y^{2}-x^{2}=36y2−x2=36

Solve the nonlinear system of equations for real solutions. - {x2+y2=25x=y2−5\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 25 \\x & = y ^ { 2 } - 5\end{aligned} \right.{x2+y2x​=25=y2−5​

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - x29+y24=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 19x2​+4y2​=1

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - x=−2(y−6)2+1x=-2(y-6)^{2}+1x=−2(y−6)2+1

Sketch the graph of the equation. - (x+1)24+(y+2)216=1\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 14(x+1)2​+16(y+2)2​=1

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - y=2(x−1)2+3y=2(x-1)^{2}+3y=2(x−1)2+3

Sketch the graph of the equation. If the graph is a parabola, find its vertex. If the graph is a circle, find its center and radius. - y=−3x2+24x−47y=-3 x^{2}+24 x-47y=−3x2+24x−47

Write an equation of the circle with the given center and radius. - (4,8);17( 4,8 ) ; \sqrt { 17 }(4,8);17​

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Sequences, Series, and the Binomial Theorem

Filters

Graph the system. - $\left\{\begin{aligned}3 x+5 y & \geq 15 \\y & \geq x^{2}+1\end{aligned}\right.$ $Graph the system. - \left\{\begin{aligned} 3 x+5 y & \geq 15 \\ y & \geq x^{2}+1 \end{aligned}\right.$

Sketch the graph of the equation. - $x^{2}+y^{2}-8 y=0$ $Sketch the graph of the equation. - x^{2}+y^{2}-8 y=0$

Write an equation of the circle with the given center and radius. -the origin; $\sqrt { 13 }$

Graph the inequality. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } \leq 1$ $Graph the inequality. - \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } \leq 1$

Graph the inequality. - $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } \geq 1$ $Graph the inequality. - \frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } \geq 1$

The graph of the equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. - $y = - 5 x ^ { 2 } - 4 x + 2$

Identify whether the equation, when graphed, will be a parabola, circle, ellipse, or hyperbola. - $16 x ^ { 2 } + 25 y ^ { 2 } = 400$

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 16 } = 1$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 65 \\4 x + 7 y = 0\end{array} \right.$

Sketch the graph of the equation. - $y^{2}-x^{2}=36$ $Sketch the graph of the equation. - y^{2}-x^{2}=36$

Solve the nonlinear system of equations for real solutions. - $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 25 \\x & = y ^ { 2 } - 5\end{aligned} \right.$

Identify the graph of the equation as an ellipse or a hyperbola. Do not graph. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Sketch the graph of the equation. - $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ $Sketch the graph of the equation. - \frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$

Write an equation of the circle with the given center and radius. - $( 4,8 ) ; \sqrt { 17 }$