Question 1

Match each equation on the left with the appropriate description of its graph on the right.
-$(y-1)^{2}+x=3$

Accepted Answer

A)  Ellipse; center $(3,1)$ 
B)  Hyperbola; center $(3,1)$ 
C)  Circle; center $(3,-1)$; radius 4 
D)  Parabola; opens downward 
E)  Circle; center $(-3,1)$; radius 4
F) Parabola; opens left 
A)  Ellipse; center $(3,1)$ 
B)  Hyperbola; center $(3,1)$ 
C)  Circle; center $(3,-1)$; radius 4 
D)  Parabola; opens downward 
E)  Circle; center $(-3,1)$; radius 4
F) Parabola; opens left

Question 2

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$x^{2}+y^{2}+4 x+4 y+8=0$

Accepted Answer

@#IMG-DLM& 
Point (c

Question 3

A gallery has the shape of the top half of an ellipse. The cross section is 13 feet high at the center and 40 feet long. Find the equation of the complete ellipse. How far apart are the foci?

Accepted Answer

The answer of A gallery has the shape of the...

Question 4

Match each equation on the left with the appropriate description of its graph on the right.
-$(x-4)^{2}+(y+3)^{2}=36$

Accepted Answer

A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$ 
A)  Ellipse; center $(-4,-3)$ 
B)  Parabola; opens right 
C)  Circle; center (4, -3$)$; radius 6 
D)  Parabola; opens upward 
E)  Circle; center $(-4,3)$; radius 6
F) Hyperbola; center $(4,-3)$

Question 5

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$\frac{(y+2)^{2}}{9}-\frac{(x-1)^{2}}{16}=1$

Accepted Answer

@#IMG-DLM& 
Hyperbola; center:

Question 6

Match each equation on the left with the appropriate description of its graph on the right.
-$(x-2)^{2}+(y+1)^{2}=9$

Accepted Answer

A)  Circle; center $(2,-1)$; radius 3 
B)  Hyperbola; center $(2,1)$ 
C)  Parabola; opens left 
D)  Circle; center $(-2,1)$; radius 3 
E)  Parabola; opens downward
F) Ellipse; center $(2,1)$ 
A)  Circle; center $(2,-1)$; radius 3 
B)  Hyperbola; center $(2,1)$ 
C)  Parabola; opens left 
D)  Circle; center $(-2,1)$; radius 3 
E)  Parabola; opens downward
F) Ellipse; center $(2,1)$

Question 7

Match each equation on the left with the appropriate description of its graph on the right.
-$(y+2)^{2}+x=6$

Accepted Answer

A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$ 
A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$

Question 8

Give the coordinates of the focus and the equation of the directrix for the parabola with equation $y=-4 x^{2}$.

Accepted Answer

The answer of Give the coordinates of the focus and...

Question 9

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$x^{2}+y^{2}+6 x-8 y-11=0$

Accepted Answer

@#IMG-DLM& 
Circle;

Question 10

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable
-$\frac{x^{2}}{64}-\frac{y^{2}}{36}=1$

Accepted Answer

@#IMG-DLM& 
Hyperbola; center:

Question 11

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$\frac{y^{2}}{9}-\frac{x^{2}}{1}=1$

Accepted Answer

@#IMG-DLM& 
Hyperbola; center:

Question 12

Planets in our solar system orbit the sun in elliptical orbits with the sun at one focus. The path of the orbit of Mercury has a major axis of length 115.8 million miles and an eccentricity of .206. (Source: NASA.) Position the center of the ellipse at the origin and determine the equation of the ellipse. What is the maximum distance between Mercury and the sun?

Accepted Answer

The answer of Planets in our solar system orbit the...

Question 13

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$\frac{(x-1)^{2}}{9}-\frac{(y+4)^{2}}{16}=1$

Accepted Answer

@#IMG-DLM& 
Hyperbola; center:

Question 14

Match each equation on the left with the appropriate description of its graph on the right.
-$(x-6)^{2}+(y+2)^{2}=25$

Accepted Answer

A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$ 
A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$

Question 15

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable.
-$x^{2}+y^{2}-6 x-4 y+13=0$

Accepted Answer

@#IMG-DLM& 
Point (c

Question 16

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable
-$y^{2}+4 x+10 y+13=0$

Accepted Answer

@#IMG-DLM& 
Parabola

Question 17

Graph $y=-\sqrt{\frac{x^{2}}{25}-1}$. Is the graph that of a function? Find the domain and range.

Accepted Answer

@#IMG-DLM& 
Yes. Dom

Question 18

Some comets orbit the sun in elliptical orbits with the sun at one focus. The path of the orbit of Halley's Comet has a major axis of length 35.8 astronomical units (AU) and an eccentricity of .967. (Source: NASA.) Position the center of the ellipse at the origin and determine the equation of the ellipse. What is the minimum distance between Halley's Comet and the sun?

Accepted Answer

The answer of Some comets orbit the sun in elliptical...

Question 19

Match each equation on the left with the appropriate description of its graph on the right.
-$(x+6)^{2}+y=2$

Accepted Answer

A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$ 
A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$

Question 20

Match each equation on the left with the appropriate description of its graph on the right.
-$(x+6)^{2}+(y-2)^{2}=25$

Accepted Answer

A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$ 
A)  Circle; center $(6,-2)$; radius 5 
B)  Hyperbola; center $(6,-2)$ 
C)  Parabola; opens left 
D)  Circle; center $(-6,2)$; radius 5 
E)  Parabola; opens downward
F) Ellipse; center $(6,2)$

Match each equation on the left with the appropriate description of its graph on the right. - $(y-1)^{2}+x=3$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}+4 x+4 y+8=0$

A gallery has the shape of the top half of an ellipse. The cross section is 13 feet high at the center and 40 feet long. Find the equation of the complete ellipse. How far apart are the foci?

Match each equation on the left with the appropriate description of its graph on the right. - $(x-4)^{2}+(y+3)^{2}=36$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{(y+2)^{2}}{9}-\frac{(x-1)^{2}}{16}=1$

Match each equation on the left with the appropriate description of its graph on the right. - $(x-2)^{2}+(y+1)^{2}=9$

Match each equation on the left with the appropriate description of its graph on the right. - $(y+2)^{2}+x=6$

Give the coordinates of the focus and the equation of the directrix for the parabola with equation $y=-4 x^{2}$ .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}+6 x-8 y-11=0$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - $\frac{x^{2}}{64}-\frac{y^{2}}{36}=1$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{y^{2}}{9}-\frac{x^{2}}{1}=1$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{(x-1)^{2}}{9}-\frac{(y+4)^{2}}{16}=1$

Match each equation on the left with the appropriate description of its graph on the right. - $(x-6)^{2}+(y+2)^{2}=25$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}-6 x-4 y+13=0$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - $y^{2}+4 x+10 y+13=0$

Graph $y=-\sqrt{\frac{x^{2}}{25}-1}$ . Is the graph that of a function? Find the domain and range.

Match each equation on the left with the appropriate description of its graph on the right. - $(x+6)^{2}+y=2$

Match each equation on the left with the appropriate description of its graph on the right. - $(x+6)^{2}+(y-2)^{2}=25$

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Limits, Derivatives, and Definite Integrals

Reference: Basic Algebraic Concepts

Filters

Exam 6: Systems and Matrices

Match each equation on the left with the appropriate description of its graph on the right. - (y−1)2+x=3(y-1)^{2}+x=3(y−1)2+x=3

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - x2+y2+4x+4y+8=0x^{2}+y^{2}+4 x+4 y+8=0x2+y2+4x+4y+8=0

A gallery has the shape of the top half of an ellipse. The cross section is 13 feet high at the center and 40 feet long. Find the equation of the complete ellipse. How far apart are the foci?

Match each equation on the left with the appropriate description of its graph on the right. - (x−4)2+(y+3)2=36(x-4)^{2}+(y+3)^{2}=36(x−4)2+(y+3)2=36

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - (y+2)29−(x−1)216=1\frac{(y+2)^{2}}{9}-\frac{(x-1)^{2}}{16}=19(y+2)2​−16(x−1)2​=1

Match each equation on the left with the appropriate description of its graph on the right. - (x−2)2+(y+1)2=9(x-2)^{2}+(y+1)^{2}=9(x−2)2+(y+1)2=9

Match each equation on the left with the appropriate description of its graph on the right. - (y+2)2+x=6(y+2)^{2}+x=6(y+2)2+x=6

Give the coordinates of the focus and the equation of the directrix for the parabola with equation y=−4x2y=-4 x^{2}y=−4x2 .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - x2+y2+6x−8y−11=0x^{2}+y^{2}+6 x-8 y-11=0x2+y2+6x−8y−11=0

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - x264−y236=1\frac{x^{2}}{64}-\frac{y^{2}}{36}=164x2​−36y2​=1

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - y29−x21=1\frac{y^{2}}{9}-\frac{x^{2}}{1}=19y2​−1x2​=1

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - (x−1)29−(y+4)216=1\frac{(x-1)^{2}}{9}-\frac{(y+4)^{2}}{16}=19(x−1)2​−16(y+4)2​=1

Match each equation on the left with the appropriate description of its graph on the right. - (x−6)2+(y+2)2=25(x-6)^{2}+(y+2)^{2}=25(x−6)2+(y+2)2=25

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - x2+y2−6x−4y+13=0x^{2}+y^{2}-6 x-4 y+13=0x2+y2−6x−4y+13=0

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - y2+4x+10y+13=0y^{2}+4 x+10 y+13=0y2+4x+10y+13=0

Graph y=−x225−1y=-\sqrt{\frac{x^{2}}{25}-1}y=−25x2​−1​ . Is the graph that of a function? Find the domain and range.

Match each equation on the left with the appropriate description of its graph on the right. - (x+6)2+y=2(x+6)^{2}+y=2(x+6)2+y=2

Match each equation on the left with the appropriate description of its graph on the right. - (x+6)2+(y−2)2=25(x+6)^{2}+(y-2)^{2}=25(x+6)2+(y−2)2=25

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Limits, Derivatives, and Definite Integrals

Reference: Basic Algebraic Concepts

Filters

Match each equation on the left with the appropriate description of its graph on the right. - $(y-1)^{2}+x=3$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}+4 x+4 y+8=0$

Match each equation on the left with the appropriate description of its graph on the right. - $(x-4)^{2}+(y+3)^{2}=36$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{(y+2)^{2}}{9}-\frac{(x-1)^{2}}{16}=1$

Match each equation on the left with the appropriate description of its graph on the right. - $(x-2)^{2}+(y+1)^{2}=9$

Match each equation on the left with the appropriate description of its graph on the right. - $(y+2)^{2}+x=6$

Give the coordinates of the focus and the equation of the directrix for the parabola with equation $y=-4 x^{2}$ .

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}+6 x-8 y-11=0$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - $\frac{x^{2}}{64}-\frac{y^{2}}{36}=1$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{y^{2}}{9}-\frac{x^{2}}{1}=1$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $\frac{(x-1)^{2}}{9}-\frac{(y+4)^{2}}{16}=1$

Match each equation on the left with the appropriate description of its graph on the right. - $(x-6)^{2}+(y+2)^{2}=25$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable. - $x^{2}+y^{2}-6 x-4 y+13=0$

Graph the relation. Identify the graph and give the the radius, center, vertices, and foci as applicable - $y^{2}+4 x+10 y+13=0$

Graph $y=-\sqrt{\frac{x^{2}}{25}-1}$ . Is the graph that of a function? Find the domain and range.

Match each equation on the left with the appropriate description of its graph on the right. - $(x+6)^{2}+y=2$

Match each equation on the left with the appropriate description of its graph on the right. - $(x+6)^{2}+(y-2)^{2}=25$