Question 1

Graph the solution set to the system of inequalities. $$\begin{array} { l } 
y  3
\end{array}$$

Accepted Answer

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

Question 2

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. $x = y ^ { 2 } + 6$

Accepted Answer

A)  Horizontal axis of symmetry; 
B)  Vertical axis of symmetry; opens left opens downward 
C)  Vertical axis of symmetry; 
D)  Horizontal axis of symmetry; opens upward opens right 
A)  Horizontal axis of symmetry; 
B)  Vertical axis of symmetry; opens left opens downward 
C)  Vertical axis of symmetry; 
D)  Horizontal axis of symmetry; opens upward opens right

Question 3

Graph the solution set to the system of nonlinear inequalities. $$\begin{array} { l } 
x > ( y + 1 ) ^ { 2 } - 4 \
x - y < 1
\end{array}$$

Accepted Answer

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

Question 4

Use the distance formula to find the distance between the two points. (4, 0) and (0, -7)

Accepted Answer

A)  65 
B)  11 
C)  $\sqrt { 65 }$ 
D)  3 
A)  65 
B)  11 
C)  $\sqrt { 65 }$ 
D)  3

Question 5

Use the equation of the parabola in standard form $x = a ( y - k ) ^ { 2 } + h$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $$x = ( y + 2 ) ^ { 2 } - 1$$

Accepted Answer

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

Question 6

Use the equation of the parabola in standard form $x = a ( y - k ) ^ { 2 } + h$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $$x = - y ^ { 2 } - 6 y - 10$$

Accepted Answer

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

Question 7

Use the distance formula to find the distance between the two points. (2, 6) and (-2, 14)

Accepted Answer

A)  12 
B)  $4 \sqrt { 5 }$ 
C)  $2 \sqrt { 3 }$ 
D)  80 
A)  12 
B)  $4 \sqrt { 5 }$ 
C)  $2 \sqrt { 3 }$ 
D)  80

Question 8

Identify the center of the ellipse $$( x + 2 ) ^ { 2 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$$ Then graph the ellipse.

Accepted Answer

The answer of Identify the center of the ellipse \[(...

Question 9

The sum of two numbers is 13. The sum of the squares of the numbers is 109. Find the numbers.

Accepted Answer

A)  5 and 8 
B)  3 and 10 
C)  0 and 13 
D)  4 and 9 
A)  5 and 8 
B)  3 and 10 
C)  0 and 13 
D)  4 and 9

Question 10

Find the midpoint of the line segment between the two given points. (-0.2, -4.5) and (-3.7, -2.1)

Accepted Answer

A)  (1.75, -1.2) 
B)  (-2.35, -2.9) 
C)  (-1.95, -1.2) 
D)  (-1.95, -3.3) 
A)  (1.75, -1.2) 
B)  (-2.35, -2.9) 
C)  (-1.95, -1.2) 
D)  (-1.95, -3.3)

Question 11

Graph the solution set. $$y \leq - 2 x ^ { 2 }$$

Accepted Answer

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

Question 12

Identify the center and radius of the circle. $$x ^ { 2 } - 8 x + y ^ { 2 } = 20$$

Accepted Answer

A)  Center: $( 0 , - 4 ) ; r = 6$ 
B)  Center: $( 4,0 ) ; r = 6$ 
C)  Center: $( 8,0 ) ; r = 36$ 
D)  Center: $( 8,0 ) ; r = 2 \sqrt { 5 }$ 
A)  Center: $( 0 , - 4 ) ; r = 6$ 
B)  Center: $( 4,0 ) ; r = 6$ 
C)  Center: $( 8,0 ) ; r = 36$ 
D)  Center: $( 8,0 ) ; r = 2 \sqrt { 5 }$

Question 13

Find the midpoint of the line segment between the two given points. (1, -2) and (-9, 2)

Accepted Answer

A)  (-8, 0) 
B)  (-2, 5) 
C)  (-3, 1) 
D)  (-4, 0) 
A)  (-8, 0) 
B)  (-2, 5) 
C)  (-3, 1) 
D)  (-4, 0)

Question 14

Determine the vertex by using the vertex formula. $$y = - \frac { 1 } { 8 } x ^ { 2 } + x + \frac { 1 } { 8 }$$

Accepted Answer

A)  $\left( 8 , \frac { 1 } { 8 } \right)$ 
B)  $\left( - 8 , - \frac { 127 } { 8 } \right)$ 
C)  $\left( - 4 , - \frac { 49 } { 8 } \right)$ 
D)  $\left( 4 , \frac { 17 } { 8 } \right)$ 
A)  $\left( 8 , \frac { 1 } { 8 } \right)$ 
B)  $\left( - 8 , - \frac { 127 } { 8 } \right)$ 
C)  $\left( - 4 , - \frac { 49 } { 8 } \right)$ 
D)  $\left( 4 , \frac { 17 } { 8 } \right)$

Question 15

Which of the following is the equation of a circle?

Accepted Answer

A)  $x ^ { 2 } - y ^ { 2 } = 81$ 
B)  $( x - 5 ) ^ { 2 } + y ^ { 2 } = 49$ 
C)  $y = 9 x ^ { 2 } + 5$ 
D)  $( x - 5 ) + ( y - 9 ) ^ { 2 } = 49$ 
A)  $x ^ { 2 } - y ^ { 2 } = 81$ 
B)  $( x - 5 ) ^ { 2 } + y ^ { 2 } = 49$ 
C)  $y = 9 x ^ { 2 } + 5$ 
D)  $( x - 5 ) + ( y - 9 ) ^ { 2 } = 49$

Question 16

Solve the system of nonlinear equations by the substitution method. $$\begin{array} { l } 
y + 2 x ^ { 2 } = 5 \
x ^ { 2 } + 3 y = - 10
\end{array}$$

Accepted Answer

A)  $\{ ( 0,5 ) , ( 3,1 ) , ( 3 , - 1 ) \}$ 
B)  $\left\{ \left( \frac { \sqrt { 5 } } { 2 } , 0 \right) , \left( - \frac { \sqrt { 5 } } { 2 } , 0 \right) \right\}$ 
C)  $\{ ( \sqrt { 5 } , - 5 ) , ( - \sqrt { 5 } , - 5 ) \}$ 
D)  {  } 
A)  $\{ ( 0,5 ) , ( 3,1 ) , ( 3 , - 1 ) \}$ 
B)  $\left\{ \left( \frac { \sqrt { 5 } } { 2 } , 0 \right) , \left( - \frac { \sqrt { 5 } } { 2 } , 0 \right) \right\}$ 
C)  $\{ ( \sqrt { 5 } , - 5 ) , ( - \sqrt { 5 } , - 5 ) \}$ 
D)  {  }

Question 17

Use the equation of the parabola in standard form $y = a ( x - h ) ^ { 2 } + k$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $$y = - 2 x ^ { 2 } - 4 x$$

Accepted Answer

A)  vertex: $( 1 , - 2 )$;
Line of symmetry $x = 1$
  
B)  vertex: $( - 1,2 )$;
Line of symmetry $x = - 1$
  
C)  vertex: $( - 1 , - 2 )$;
Line of symmetry $x = - 1$
  
D)  vertex: $( 1,2 )$;
Line of symmetry $x = 1$
  
A)  vertex: $( 1 , - 2 )$;
Line of symmetry $x = 1$
  
B)  vertex: $( - 1,2 )$;
Line of symmetry $x = - 1$
  
C)  vertex: $( - 1 , - 2 )$;
Line of symmetry $x = - 1$
  
D)  vertex: $( 1,2 )$;
Line of symmetry $x = 1$

Question 18

A map of a hiking area is drawn so that the Visitor Center is at the origin of a rectangular grid. Two hikers are located at positions (-3, 1) and (2, 3) with respect to the Visitor Center where all units are in Miles. A campground is located exactly halfway between the hikers. What are the coordinates of the
Campground?

Accepted Answer

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

Question 19

Graph the solution set to the system of nonlinear inequalities. $$\begin{array} { l } 
y > x ^ { 3 } \
y  0
\end{array}$$

Accepted Answer

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

Question 20

Solve the system of nonlinear equations by the addition method. $$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
2 x ^ { 2 } + y ^ { 2 } = 50
\end{array}$$

Accepted Answer

A)  $\{ ( 0,5 ) \}$ 
B)  $\{ ( 5,0 ) \}$ 
C)  $\{ ( - 5,0 ) , ( 5,0 ) \}$ 
D)  $\{ ( 0 , - 5 ) , ( 0,5 ) \}$ 
A)  $\{ ( 0,5 ) \}$ 
B)  $\{ ( 5,0 ) \}$ 
C)  $\{ ( - 5,0 ) , ( 5,0 ) \}$ 
D)  $\{ ( 0 , - 5 ) , ( 0,5 ) \}$

Graph the solution set to the system of inequalities. y< x>3

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. $x = y ^ { 2 } + 6$

Graph the solution set to the system of nonlinear inequalities. x>(y+1-4 x-y<1

Use the distance formula to find the distance between the two points. (4, 0) and (0, -7)

Use the equation of the parabola in standard form $x = a ( y - k ) ^ { 2 } + h$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $x = ( y + 2 ) ^ { 2 } - 1$

Use the equation of the parabola in standard form $x = a ( y - k ) ^ { 2 } + h$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $x = - y ^ { 2 } - 6 y - 10$

Use the distance formula to find the distance between the two points. (2, 6) and (-2, 14)

Identify the center of the ellipse $( x + 2 ) ^ { 2 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ Then graph the ellipse.

The sum of two numbers is 13. The sum of the squares of the numbers is 109. Find the numbers.

Find the midpoint of the line segment between the two given points. (-0.2, -4.5) and (-3.7, -2.1)

Graph the solution set. $y \leq - 2 x ^ { 2 }$

Identify the center and radius of the circle. $x ^ { 2 } - 8 x + y ^ { 2 } = 20$

Find the midpoint of the line segment between the two given points. (1, -2) and (-9, 2)

Determine the vertex by using the vertex formula. $y = - \frac { 1 } { 8 } x ^ { 2 } + x + \frac { 1 } { 8 }$

Which of the following is the equation of a circle?

Solve the system of nonlinear equations by the substitution method. y+2=5 +3y=-10

Use the equation of the parabola in standard form $y = a ( x - h ) ^ { 2 } + k$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $y = - 2 x ^ { 2 } - 4 x$

Graph the solution set to the system of nonlinear inequalities. y> y<8 x>0

Solve the system of nonlinear equations by the addition method. +=25 2+=50

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

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Exam 9: Conic Sections

Graph the solution set to the system of inequalities. y< x>3

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. x=y2+6x = y ^ { 2 } + 6x=y2+6

Graph the solution set to the system of nonlinear inequalities. x>(y+1-4 x-y<1

Use the distance formula to find the distance between the two points. (4, 0) and (0, -7)

Use the equation of the parabola in standard form x=a(y−k)2+hx = a ( y - k ) ^ { 2 } + hx=a(y−k)2+h to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. x=(y+2)2−1x = ( y + 2 ) ^ { 2 } - 1x=(y+2)2−1

Use the distance formula to find the distance between the two points. (2, 6) and (-2, 14)

Identify the center of the ellipse (x+2)2+(y+2)225=1( x + 2 ) ^ { 2 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1(x+2)2+25(y+2)2​=1 Then graph the ellipse.

The sum of two numbers is 13. The sum of the squares of the numbers is 109. Find the numbers.

Find the midpoint of the line segment between the two given points. (-0.2, -4.5) and (-3.7, -2.1)

Graph the solution set. y≤−2x2y \leq - 2 x ^ { 2 }y≤−2x2

Identify the center and radius of the circle. x2−8x+y2=20x ^ { 2 } - 8 x + y ^ { 2 } = 20x2−8x+y2=20

Find the midpoint of the line segment between the two given points. (1, -2) and (-9, 2)

Determine the vertex by using the vertex formula. y=−18x2+x+18y = - \frac { 1 } { 8 } x ^ { 2 } + x + \frac { 1 } { 8 }y=−81​x2+x+81​

Which of the following is the equation of a circle?

Solve the system of nonlinear equations by the substitution method. y+2=5 +3y=-10

Use the equation of the parabola in standard form y=a(x−h)2+ky = a ( x - h ) ^ { 2 } + ky=a(x−h)2+k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. y=−2x2−4xy = - 2 x ^ { 2 } - 4 xy=−2x2−4x

Graph the solution set to the system of nonlinear inequalities. y> y<8 x>0

Solve the system of nonlinear equations by the addition method. +=25 2+=50

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. $x = y ^ { 2 } + 6$

Use the equation of the parabola in standard form $x = a ( y - k ) ^ { 2 } + h$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $x = ( y + 2 ) ^ { 2 } - 1$

Identify the center of the ellipse $( x + 2 ) ^ { 2 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ Then graph the ellipse.

Graph the solution set. $y \leq - 2 x ^ { 2 }$

Identify the center and radius of the circle. $x ^ { 2 } - 8 x + y ^ { 2 } = 20$

Determine the vertex by using the vertex formula. $y = - \frac { 1 } { 8 } x ^ { 2 } + x + \frac { 1 } { 8 }$

Use the equation of the parabola in standard form $y = a ( x - h ) ^ { 2 } + k$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $y = - 2 x ^ { 2 } - 4 x$