Question 1

Determine whether the graph of the quadratic function opens up or down.
-$f ( x ) = - 8 x ^ { 2 } + 9 x + 1$

Accepted Answer

A) down 
B) up 
A) down 
B) up

Question 2

Solve the problem.
-Find the equation of the ellipse, if (-7, -3)and (5, -3)are the endpoints of the major axis and (-1, -6)and (-1, 0) are the endpoints of the minor axis.

Accepted Answer

A)  $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$ 
A)  $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$

Question 3

Find all real solutions to the system of equations using the substitution method.
-$\begin{array} { l } 
x y - x ^ { 2 } = - 20 \
x - 2 y = 3
\end{array}$

Accepted Answer

A)  $( - 5 , - 1 ) , \left( 8 , \frac { 11 } { 2 } \right)$ 
B)  $( - 5 , - 1 ) , \left( \frac { 11 } { 2 } , 8 \right)$ 
C)  $( 5,1 ) , \left( - 8 , - \frac { 11 } { 2 } \right)$ 
D)  $( 5,1 ) , \left( - \frac { 11 } { 2 } , - 8 \right)$ 
A)  $( - 5 , - 1 ) , \left( 8 , \frac { 11 } { 2 } \right)$ 
B)  $( - 5 , - 1 ) , \left( \frac { 11 } { 2 } , 8 \right)$ 
C)  $( 5,1 ) , \left( - 8 , - \frac { 11 } { 2 } \right)$ 
D)  $( 5,1 ) , \left( - \frac { 11 } { 2 } , - 8 \right)$

Question 4

Write the equation of the circle with the given center and radius.
-Center (-10, 8), radiuss $\sqrt { 5 }$

Accepted Answer

A)  $( x - 8 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 25$ 
B)  $( x + 10 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 5$ 
C)  $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$ 
D)  $( x - 10 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 5$ 
A)  $( x - 8 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 25$ 
B)  $( x + 10 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 5$ 
C)  $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$ 
D)  $( x - 10 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 5$

Question 5

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain bothth $x ^ { 2 }$ 2 and $y ^ { 2 }$ terms, divide both terms, divide bothsides of the equation by the constant term to put the equation in a more recognizable form.
-$5 x ^ { 2 } + 8 y ^ { 2 } = 36$

Accepted Answer

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

Question 6

Determine the midpoint of the line segment between the pair of points.
-$( 9 \sqrt { 5 } , 6 \sqrt { 5 } ) \text { and } ( 14 \sqrt { 5 } , 11 \sqrt { 5 } )$

Accepted Answer

A)  $\left( \frac { 5 \sqrt { 5 } } { 2 } , \frac { 5 \sqrt { 5 } } { 2 } \right)$ 
B)  $( 23 \sqrt { 5 } , 17 \sqrt { 5 } )$ 
C)  $\left( \frac { - 5 \sqrt { 5 } } { 2 } , \frac { - 5 \sqrt { 5 } } { 2 } \right)$ 
D)  $\left( \frac { 23 \sqrt { 5 } } { 2 } , \frac { 17 \sqrt { 5 } } { 2 } \right)$ 
A)  $\left( \frac { 5 \sqrt { 5 } } { 2 } , \frac { 5 \sqrt { 5 } } { 2 } \right)$ 
B)  $( 23 \sqrt { 5 } , 17 \sqrt { 5 } )$ 
C)  $\left( \frac { - 5 \sqrt { 5 } } { 2 } , \frac { - 5 \sqrt { 5 } } { 2 } \right)$ 
D)  $\left( \frac { 23 \sqrt { 5 } } { 2 } , \frac { 17 \sqrt { 5 } } { 2 } \right)$

Question 7

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { c } 
2 x ^ { 2 } + y ^ { 2 } = 17 \
3 x ^ { 2 } - 2 y ^ { 2 } = - 6
\end{array}$

Accepted Answer

A) (2, -3), (-2, 3) 
B) (1, 3), (1, -3), (-1, 3), (-1, -3) 
C) (1, 3), (-1, -3) 
D) (2, 3), (2, -3), (-2, 3), (-2, -3) 
A) (2, -3), (-2, 3) 
B) (1, 3), (1, -3), (-1, 3), (-1, -3) 
C) (1, 3), (-1, -3) 
D) (2, 3), (2, -3), (-2, 3), (-2, -3)

Question 8

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.
-$x = 2 y ^ { 2 } + 12 y + 17$

Accepted Answer

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

Question 9

Find all real solutions to the system of equations using the substitution method.
-$\begin{array} { r } 
x y = 12 \
x + y = 7
\end{array}$

Accepted Answer

A) (4, -3), (3, -4) 
B) (4, 3), (3, 4) 
C) (-4, 3), (-3, 4) 
D) (-4, -3), (-3, -4) 
A) (4, -3), (3, -4) 
B) (4, 3), (3, 4) 
C) (-4, 3), (-3, 4) 
D) (-4, -3), (-3, -4)

Question 10

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 100 \
x ^ { 2 } - y ^ { 2 } = 100
\end{array}$

Accepted Answer

A) (-10, 0), (-10, 10) 
B) (10, 0), (-10, 0) 
C) (10, 10), (-10, 10) 
D) (10, 0), (10, 10) 
A) (-10, 0), (-10, 10) 
B) (10, 0), (-10, 0) 
C) (10, 10), (-10, 10) 
D) (10, 0), (10, 10)

Question 11

Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain bothth $x ^ { 2 }$ 2 and $y ^ { 2 }$ terms, divide both terms, divide bothsides of the equation by the constant term to put the equation in a more recognizable form.
-$5 x ^ { 2 } + 5 y ^ { 2 } - 12 y = 2$

Accepted Answer

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

Question 12

Name the conic.
-

Accepted Answer

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

Question 13

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.
-$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 16 } = 1$

Accepted Answer

A)  $y= \pm 2 x$

B)  $y = \pm 2 x$

C)  $y = \pm \frac { 1 } { 2 } x$

D)  $y = \pm \frac { 1 } { 2 } x$

A)  $y= \pm 2 x$

B)  $y = \pm 2 x$

C)  $y = \pm \frac { 1 } { 2 } x$

D)  $y = \pm \frac { 1 } { 2 } x$

Question 14

Find all real solutions to the system of equations using the substitution method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 41 \
x - y = 1
\end{array}$

Accepted Answer

A) (4, -5), (5, -4) 
B) (4, 5), (5, 4) 
C) (-4, -5), (5, 4) 
D) (-4, 5), (-5, 4) 
A) (4, -5), (5, -4) 
B) (4, 5), (5, 4) 
C) (-4, -5), (5, 4) 
D) (-4, 5), (-5, 4)

Question 15

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 64 \
y < ( x - 2 ) ^ { 2 } + 3
\end{array}$

Accepted Answer

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

Question 16

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } > 1 \
\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } \leq 1
\end{array}$

Accepted Answer

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

Question 17

Graph the inequality.
-$x \geq ( y - 1 ) ^ { 2 } - 5$

Accepted Answer

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

Question 18

Graph the equation.
-$16 ( x + 1 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

Accepted Answer

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

Question 19

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.
-$y = - 4 x ^ { 2 } - 32 x - 66$

Accepted Answer

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

Question 20

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
x y \leq 3 \
- 3 x - y \leq 6
\end{array}$

Accepted Answer

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

Determine whether the graph of the quadratic function opens up or down. - $f ( x ) = - 8 x ^ { 2 } + 9 x + 1$

Solve the problem. -Find the equation of the ellipse, if (-7, -3)and (5, -3)are the endpoints of the major axis and (-1, -6)and (-1, 0) are the endpoints of the minor axis.

Find all real solutions to the system of equations using the substitution method. - xy-=-20 x-2y=3

Write the equation of the circle with the given center and radius. -Center (-10, 8), radiuss $\sqrt { 5 }$

Determine the midpoint of the line segment between the pair of points. - $( 9 \sqrt { 5 } , 6 \sqrt { 5 } ) \text { and } ( 14 \sqrt { 5 } , 11 \sqrt { 5 } )$

Find all real solutions to the system of equations using the addition method. - 2+=17 3-2=-6

Find all real solutions to the system of equations using the substitution method. - xy=12 x+y=7

Find all real solutions to the system of equations using the addition method. - +=100 -=100

Name the conic. -

Find all real solutions to the system of equations using the substitution method. - +=41 x-y=1

Determine the solution to the system of inequalities. - +\leq64 y<(x-2+3 $Determine the solution to the system of inequalities. - \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 64 \\ y < ( x - 2 ) ^ { 2 } + 3 \end{array}$

Determine the solution to the system of inequalities. - ->1 +\leq1 $Determine the solution to the system of inequalities. - \begin{array} { l } x ^ { 2 } - y ^ { 2 } > 1 \\ \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } \leq 1 \end{array}$

Graph the inequality. - $x \geq ( y - 1 ) ^ { 2 } - 5$ $Graph the inequality. - x \geq ( y - 1 ) ^ { 2 } - 5$

Graph the equation. - $16 ( x + 1 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$ $Graph the equation. - 16 ( x + 1 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

Determine the solution to the system of inequalities. - xy\leq3 -3x-y\leq6 $Determine the solution to the system of inequalities. - \begin{array} { l } x y \leq 3 \\ - 3 x - y \leq 6 \end{array}$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Sequences, Series, and Probability

Filters

Exam 11: Conic Sections

Determine whether the graph of the quadratic function opens up or down. - f(x)=−8x2+9x+1f ( x ) = - 8 x ^ { 2 } + 9 x + 1f(x)=−8x2+9x+1

Solve the problem. -Find the equation of the ellipse, if (-7, -3)and (5, -3)are the endpoints of the major axis and (-1, -6)and (-1, 0) are the endpoints of the minor axis.

Find all real solutions to the system of equations using the substitution method. - xy-=-20 x-2y=3

Write the equation of the circle with the given center and radius. -Center (-10, 8), radiuss 5\sqrt { 5 }5​

Determine the midpoint of the line segment between the pair of points. - (95,65) and (145,115)( 9 \sqrt { 5 } , 6 \sqrt { 5 } ) \text { and } ( 14 \sqrt { 5 } , 11 \sqrt { 5 } )(95​,65​) and (145​,115​)

Find all real solutions to the system of equations using the addition method. - 2+=17 3-2=-6

Write the equation in the form y=a(x−h)2+k or x=a(y−k)2+h\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}y=a(x−h)2+k or x=a(y−k)2+h h a nd then graph the equation. - x=2y2+12y+17x = 2 y ^ { 2 } + 12 y + 17x=2y2+12y+17

Find all real solutions to the system of equations using the substitution method. - xy=12 x+y=7

Find all real solutions to the system of equations using the addition method. - +=100 -=100

Name the conic. -

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the equation. - y24−x216=1\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 16 } = 14y2​−16x2​=1

Find all real solutions to the system of equations using the substitution method. - +=41 x-y=1

Determine the solution to the system of inequalities. - +\leq64 y<(x-2+3

Determine the solution to the system of inequalities. - ->1 +\leq1

Graph the inequality. - x≥(y−1)2−5x \geq ( y - 1 ) ^ { 2 } - 5x≥(y−1)2−5

Graph the equation. - 16(x+1)2+9(y−1)2=14416 ( x + 1 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 14416(x+1)2+9(y−1)2=144

Write the equation in the form y=a(x−h)2+k or x=a(y−k)2+h\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}y=a(x−h)2+k or x=a(y−k)2+h h a nd then graph the equation. - y=−4x2−32x−66y = - 4 x ^ { 2 } - 32 x - 66y=−4x2−32x−66

Determine the solution to the system of inequalities. - xy\leq3 -3x-y\leq6

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Sequences, Series, and Probability

Filters

Determine whether the graph of the quadratic function opens up or down. - $f ( x ) = - 8 x ^ { 2 } + 9 x + 1$

Write the equation of the circle with the given center and radius. -Center (-10, 8), radiuss $\sqrt { 5 }$

Determine the midpoint of the line segment between the pair of points. - $( 9 \sqrt { 5 } , 6 \sqrt { 5 } ) \text { and } ( 14 \sqrt { 5 } , 11 \sqrt { 5 } )$

Determine the solution to the system of inequalities. - +\leq64 y<(x-2+3 $Determine the solution to the system of inequalities. - \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 64 \\ y < ( x - 2 ) ^ { 2 } + 3 \end{array}$

Determine the solution to the system of inequalities. - ->1 +\leq1 $Determine the solution to the system of inequalities. - \begin{array} { l } x ^ { 2 } - y ^ { 2 } > 1 \\ \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } \leq 1 \end{array}$

Graph the inequality. - $x \geq ( y - 1 ) ^ { 2 } - 5$ $Graph the inequality. - x \geq ( y - 1 ) ^ { 2 } - 5$

Graph the equation. - $16 ( x + 1 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$ $Graph the equation. - 16 ( x + 1 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

Determine the solution to the system of inequalities. - xy\leq3 -3x-y\leq6 $Determine the solution to the system of inequalities. - \begin{array} { l } x y \leq 3 \\ - 3 x - y \leq 6 \end{array}$