Question 1

Graph the hyperbola $-$ 9 x 2 + 36 x + 4 y 2 + 24 y $-$ 16 = 0.

Accepted Answer

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

Question 2

Identify the graph of the parabola. y = x  2 + 10 x + 21

Accepted Answer

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

Question 3

Graph the parabola. $y = ( x - 4 ) ^ { 2 }$

Accepted Answer

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

Question 4

Graph the parabola. $y = 4 ( x - 1 ) ^ { 2 } - 2$

Accepted Answer

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

Question 5

The point of intersection of the major and minor axes is called the vertex of the ellipse.

Accepted Answer

A) True 
 B)False

Question 6

Graph the hyperbola 2 y 2 $-$ 25 x 2 = 50.

Accepted Answer

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

Question 7

Graph the parabola. $y = \frac { 1 } { 3 } x ^ { 2 } - 4$

Accepted Answer

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

Question 8

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph.
-symmetry with respect to the x axis

Accepted Answer

A)  $x ^ { 2 } - 3 x - y ^ { 2 } = 4$ 
B)  $y = x ^ { 4 } - x ^ { 2 } + 3$ 
C)  $y = 2 x$ 
A)  $x ^ { 2 } - 3 x - y ^ { 2 } = 4$ 
B)  $y = x ^ { 4 } - x ^ { 2 } + 3$ 
C)  $y = 2 x$

Question 9

Find the equation of the circle that passes through the origin and has its center at ( $-$ 8, 6).

Accepted Answer

The answer of Find the equation of the circle that...

Question 10

Identify the graph of the ellipse. 9 x 2 + 4 y 2 $-$ 24 y + 11 = 0

Accepted Answer

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

Question 11

Find the length of a radius of the circle. 64 x 2 + 64 y 2 $-$ 16 x $-$ 112 y $-$ 2,446 = 0

Accepted Answer

A)  $r = 1,521$ 
B)  $r = 1$ 
C)  $r = \sqrt { 39 }$ 
D)  $r = 3 \sqrt { 39 }$ 
E)  $r = 39$ 
A)  $r = 1,521$ 
B)  $r = 1$ 
C)  $r = \sqrt { 39 }$ 
D)  $r = 3 \sqrt { 39 }$ 
E)  $r = 39$

Question 12

For all hyperbolas, the asymptotes intersect each other at the origin.

Accepted Answer

A) True 
 B)False

Question 13

Find the length of a radius of each circle. Match each of the equations with length of a radius to obtain a true statement.
-$r = \sqrt { 3 }$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 3$ 
B)  $x ^ { 2 } + y ^ { 2 } + 14 x + 6 y + 39 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 12 x + 20 y + 101 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 24 x - 32 y = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } = 3$ 
B)  $x ^ { 2 } + y ^ { 2 } + 14 x + 6 y + 39 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 12 x + 20 y + 101 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 24 x - 32 y = 0$

Question 14

For the equation $8 x ^ { 2 } + 2 y ^ { 2 } = 32$ , the major axis is vertical.

Accepted Answer

A) True 
 B)False

Question 15

The graphs of equations of the form xy = k , where k is a nonzero constant, are also hyperbolas, sometimes referred to as rectangular hyperbolas. Graph the hyperbola xy = $-$ 2.

Accepted Answer

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

Question 16

Find the slope of the line determined by the points ( $-$ 4, 0) and (0, $-$ 7).

Accepted Answer

A)  $\frac { 7 } { 4 }$ 
B)  $\frac { 4 } { 7 }$ 
C)  $- \frac { 7 } { 4 }$ 
D)  0 
A)  $\frac { 7 } { 4 }$ 
B)  $\frac { 4 } { 7 }$ 
C)  $- \frac { 7 } { 4 }$ 
D)  0

Question 17

Find the distance between the points (14, 9) and (-1, -9).

Accepted Answer

A)  $\sqrt { 183 }$ 
B)  $3 \sqrt { 61 }$ 
C)  $\sqrt { 61 }$ 
D)  61 
A)  $\sqrt { 183 }$ 
B)  $3 \sqrt { 61 }$ 
C)  $\sqrt { 61 }$ 
D)  61

Question 18

Graph the parabola. $y = - 2 ( x - 2 ) ^ { 2 } - 3$

Accepted Answer

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

Question 19

Find the distance between the points (9, 11) and (-6, -7). Express the answers in simplest radical form.

Accepted Answer

The answer of Find the distance between the points (9,...

Question 20

Graph the equation. $y = - x ^ { 4 }$

Accepted Answer

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

Graph the hyperbola $-$ 9 x 2 + 36 x + 4 y 2 + 24 y $-$ 16 = 0.

Identify the graph of the parabola. y = x ² + 10 x + 21

Graph the parabola. $y = ( x - 4 ) ^ { 2 }$

Graph the parabola. $y = 4 ( x - 1 ) ^ { 2 } - 2$

The point of intersection of the major and minor axes is called the vertex of the ellipse.

Graph the hyperbola 2 y 2 $-$ 25 x 2 = 50.

Graph the parabola. $y = \frac { 1 } { 3 } x ^ { 2 } - 4$

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph. -symmetry with respect to the x axis

Find the equation of the circle that passes through the origin and has its center at ( $-$ 8, 6).

Identify the graph of the ellipse. 9 x 2 + 4 y 2 $-$ 24 y + 11 = 0

Find the length of a radius of the circle. 64 x 2 + 64 y 2 $-$ 16 x $-$ 112 y $-$ 2,446 = 0

For all hyperbolas, the asymptotes intersect each other at the origin.

Find the length of a radius of each circle. Match each of the equations with length of a radius to obtain a true statement. - $r = \sqrt { 3 }$

For the equation $8 x ^ { 2 } + 2 y ^ { 2 } = 32$ , the major axis is vertical.

The graphs of equations of the form xy = k , where k is a nonzero constant, are also hyperbolas, sometimes referred to as rectangular hyperbolas. Graph the hyperbola xy = $-$ 2.

Find the slope of the line determined by the points ( $-$ 4, 0) and (0, $-$ 7).

Find the distance between the points (14, 9) and (-1, -9).

Graph the parabola. $y = - 2 ( x - 2 ) ^ { 2 } - 3$

Find the distance between the points (9, 11) and (-6, -7). Express the answers in simplest radical form.

Graph the equation. $y = - x ^ { 4 }$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 12: Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Graph the hyperbola −-− 9 x 2 + 36 x + 4 y 2 + 24 y −-− 16 = 0.

Identify the graph of the parabola. y = x 2 + 10 x + 21

Graph the parabola. y=(x−4)2y = ( x - 4 ) ^ { 2 }y=(x−4)2

Graph the parabola. y=4(x−1)2−2y = 4 ( x - 1 ) ^ { 2 } - 2y=4(x−1)2−2

The point of intersection of the major and minor axes is called the vertex of the ellipse.

Graph the hyperbola 2 y 2 −-− 25 x 2 = 50.

Graph the parabola. y=13x2−4y = \frac { 1 } { 3 } x ^ { 2 } - 4y=31​x2−4

Match each equation with the type of symmetry exhibited by its graph. Do not sketch the graph. -symmetry with respect to the x axis

Find the equation of the circle that passes through the origin and has its center at ( −-− 8, 6).

Identify the graph of the ellipse. 9 x 2 + 4 y 2 −-− 24 y + 11 = 0

Find the length of a radius of the circle. 64 x 2 + 64 y 2 −-− 16 x −-− 112 y −-− 2,446 = 0

For all hyperbolas, the asymptotes intersect each other at the origin.

Find the length of a radius of each circle. Match each of the equations with length of a radius to obtain a true statement. - r=3r = \sqrt { 3 }r=3​

For the equation 8x2+2y2=328 x ^ { 2 } + 2 y ^ { 2 } = 328x2+2y2=32 , the major axis is vertical.

The graphs of equations of the form xy = k , where k is a nonzero constant, are also hyperbolas, sometimes referred to as rectangular hyperbolas. Graph the hyperbola xy = −-− 2.

Find the slope of the line determined by the points ( −-− 4, 0) and (0, −-− 7).

Find the distance between the points (14, 9) and (-1, -9).

Graph the parabola. y=−2(x−2)2−3y = - 2 ( x - 2 ) ^ { 2 } - 3y=−2(x−2)2−3

Find the distance between the points (9, 11) and (-6, -7). Express the answers in simplest radical form.

Graph the equation. y=−x4y = - x ^ { 4 }y=−x4

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Graph the hyperbola $-$ 9 x 2 + 36 x + 4 y 2 + 24 y $-$ 16 = 0.

Identify the graph of the parabola. y = x ² + 10 x + 21

Graph the parabola. $y = ( x - 4 ) ^ { 2 }$

Graph the parabola. $y = 4 ( x - 1 ) ^ { 2 } - 2$

Graph the hyperbola 2 y 2 $-$ 25 x 2 = 50.

Graph the parabola. $y = \frac { 1 } { 3 } x ^ { 2 } - 4$

Find the equation of the circle that passes through the origin and has its center at ( $-$ 8, 6).

Identify the graph of the ellipse. 9 x 2 + 4 y 2 $-$ 24 y + 11 = 0

Find the length of a radius of the circle. 64 x 2 + 64 y 2 $-$ 16 x $-$ 112 y $-$ 2,446 = 0

Find the length of a radius of each circle. Match each of the equations with length of a radius to obtain a true statement. - $r = \sqrt { 3 }$

For the equation $8 x ^ { 2 } + 2 y ^ { 2 } = 32$ , the major axis is vertical.

The graphs of equations of the form xy = k , where k is a nonzero constant, are also hyperbolas, sometimes referred to as rectangular hyperbolas. Graph the hyperbola xy = $-$ 2.

Find the slope of the line determined by the points ( $-$ 4, 0) and (0, $-$ 7).

Graph the parabola. $y = - 2 ( x - 2 ) ^ { 2 } - 3$

Graph the equation. $y = - x ^ { 4 }$