# Elementary and Intermediate Algebra

## Educators

### Problem 1

a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$(x-2)^{2}+(y+5)^{2}=9$$

Heather Z.

### Problem 2

Match the equation with the center or vertex of its graph, listed in the column on the right.
a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$(x+2)^{2}+(y-5)^{2}=9$$

Heather Z.

### Problem 3

Match the equation with the center or vertex of its graph, listed in the column on the right.
a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$(x-5)^{2}+(y+2)^{2}=9$$

Heather Z.

### Problem 4

Match the equation with the center or vertex of its graph, listed in the column on the right.
a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$(x+5)^{2}+(y-2)^{2}=9$$

Heather Z.

### Problem 5

Match the equation with the center or vertex of its graph, listed in the column on the right.
a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$y=(x-2)^{2}-5$$

Heather Z.

### Problem 6

Match the equation with the center or vertex of its graph, listed in the column on the right.
a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$y=(x-5)^{2}-2$$

Heather Z.

### Problem 7

Match the equation with the center or vertex of its graph, listed in the column on the right.
a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$x=(y-2)^{2}-5$$

Heather Z.

### Problem 8

Match the equation with the center or vertex of its graph, listed in the column on the right.
a) Vertex: $(-2,5)$
b) Vertex: $(5,-2)$
c) Vertex: $(2,-5)$
d) Vertex: $(-5,2)$
e) Center: $(-2,5)$
f) Center: $(2,-5)$
g) Center: $(5,-2)$
h) Center: $(-5,2)$
$$x=(y-5)^{2}-2$$

Heather Z.

### Problem 9

Graph. Be sure to label each vertex.
$$y=-x^{2}$$

Heather Z.

### Problem 10

Graph. Be sure to label each vertex.
$$y=2 x^{2}$$

Heather Z.

### Problem 11

Graph. Be sure to label each vertex.
$$y=-x^{2}+4 x-5$$

Heather Z.

### Problem 12

Graph. Be sure to label each vertex.
$$x=4-3 y-y^{2}$$

Heather Z.

### Problem 13

Graph. Be sure to label each vertex.
$$x=y^{2}-4 y+2$$

Heather Z.

### Problem 14

Graph. Be sure to label each vertex.
$$y=x^{2}+2 x+3$$

Heather Z.

### Problem 15

Graph. Be sure to label each vertex.
$$x=y^{2}+3$$

Heather Z.

### Problem 16

Graph. Be sure to label each vertex.
$$x=-y^{2}$$

Heather Z.

### Problem 17

Graph. Be sure to label each vertex.
$$x=2 y^{2}$$

Heather Z.

### Problem 18

Graph. Be sure to label each vertex.
$$x=y^{2}-1$$

Heather Z.

### Problem 19

Graph. Be sure to label each vertex.
$$x=-y^{2}-4 y$$

Heather Z.

### Problem 20

Graph. Be sure to label each vertex.
$$x=y^{2}+3 y$$

Heather Z.

### Problem 21

Graph. Be sure to label each vertex.
$$y=x^{2}-2 x+1$$

Heather Z.

### Problem 22

Graph. Be sure to label each vertex.
$$y=x^{2}+2 x+1$$

Heather Z.

### Problem 23

Graph. Be sure to label each vertex.
$$x=-\frac{1}{2} y^{2}$$

Heather Z.

### Problem 24

Graph. Be sure to label each vertex.
$$y=-\frac{1}{2} x^{2}$$

Heather Z.

### Problem 25

Graph. Be sure to label each vertex.
$$x=-y^{2}+2 y-1$$

Heather Z.

### Problem 26

Graph. Be sure to label each vertex.
$$x=-y^{2}-2 y+3$$

Heather Z.

### Problem 27

Graph. Be sure to label each vertex.
$$x=-2 y^{2}-4 y+1$$

Heather Z.

### Problem 28

Graph. Be sure to label each vertex.
$$x=2 y^{2}+4 y-1$$

Heather Z.

### Problem 29

Find an equation of the circle satisfying the given conditions.
Center $(0,0),$ radius 6

Heather Z.

### Problem 30

Find an equation of the circle satisfying the given conditions.
Center $(0,0),$ radius 5

Heather Z.

### Problem 31

Find an equation of the circle satisfying the given conditions.
Center $(7,3),$ radius $\sqrt{5}$

Heather Z.

### Problem 32

Find an equation of the circle satisfying the given conditions.
Center $(5,6),$ radius $\sqrt{2}$

Heather Z.

### Problem 33

Find an equation of the circle satisfying the given conditions.
Center $(-4 \text { 3) radius } 4 \text { ) } \sqrt{3}$

Heather Z.

### Problem 34

Find an equation of the circle satisfying the given conditions.
Center $(-2,7),$ radius $2 \sqrt{5}$

Heather Z.

### Problem 35

Find an equation of the circle satisfying the given conditions.
Center $(-7,-2),$ radius $5 \sqrt{2}$

Heather Z.

### Problem 36

Find an equation of the circle satisfying the given conditions.
Center $(-5,-8),$ radius $3 \sqrt{2}$

Heather Z.

### Problem 37

Find an equation of the circle satisfying the given conditions.
Center $(0,0),$ passing through $(-3,4)$

Heather Z.

### Problem 38

Center $(0,0),$ passing through $(11,-10)$

Heather Z.

### Problem 39

Find an equation of the circle satisfying the given conditions.
Center $(-4,1),$ passing through $(-2,5)$

Heather Z.

### Problem 40

Find an equation of the circle satisfying the given conditions.
Center $(-1,-3),$ passing through $(-4,2)$

Heather Z.

### Problem 41

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}=64$$

Heather Z.

### Problem 42

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}=36$$

Heather Z.

### Problem 43

Find the center and the radius of each circle. Then graph the circle.
$$(x+1)^{2}+(y+3)^{2}=36$$

Heather Z.

### Problem 44

Find the center and the radius of each circle. Then graph the circle.
$$(x-2)^{2}+(y+3)^{2}=4$$

Heather Z.

### Problem 45

Find the center and the radius of each circle. Then graph the circle.
$$(x-4)^{2}+(y+3)^{2}=10$$

Heather Z.

### Problem 46

Find the center and the radius of each circle. Then graph the circle.
$$(x+5)^{2}+(y-1)^{2}=15$$

Heather Z.

### Problem 47

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}=10$$

Heather Z.

### Problem 48

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}=7$$

Heather Z.

### Problem 49

Find the center and the radius of each circle. Then graph the circle.
$$(x-5)^{2}+y^{2}=\frac{1}{4}$$

Heather Z.

### Problem 50

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+(y-1)^{2}=\frac{1}{25}$$

Heather Z.

### Problem 51

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}+8 x-6 y-15=0$$

Heather Z.

### Problem 52

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}+6 x-4 y-15=0$$

Heather Z.

### Problem 53

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}-8 x+2 y+13=0$$

Heather Z.

### Problem 54

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}+6 x+4 y+12=0$$

Heather Z.

### Problem 55

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}+10 y-75=0$$

Heather Z.

### Problem 56

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}-8 x-84=0$$

Heather Z.

### Problem 57

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}+7 x-3 y-10=0$$

Heather Z.

### Problem 58

Find the center and the radius of each circle. Then graph the circle.
$$x^{2}+y^{2}-21 x-33 y+17=0$$

Heather Z.

### Problem 59

Find the center and the radius of each circle. Then graph the circle.
$$36 x^{2}+36 y^{2}=1$$

Heather Z.

### Problem 60

Find the center and the radius of each circle. Then graph the circle.
$$4 x^{2}+4 y^{2}=1$$

Heather Z.

### Problem 61

Graph using a graphing calculator.
$$x^{2}+y^{2}-16=0$$

Heather Z.

### Problem 62

Graph using a graphing calculator.
$$4 x^{2}+4 y^{2}=100$$

Heather Z.

### Problem 63

Graph using a graphing calculator.
$$x^{2}+y^{2}+14 x-16 y+54=0$$

Heather Z.

### Problem 64

Graph using a graphing calculator.
$$x^{2}+y^{2}-10 x-11=0$$

Heather Z.

### Problem 65

Does the graph of an equation of a circle include the point that is the center? Why or why not?

Heather Z.

### Problem 66

Is a point a conic section? Why or why not?

Heather Z.

### Problem 67

To prepare for Section $13.2,$ review solving quadratic equations (Section $11.1)$
Solve for $x$ or for $y . $$\frac{y^{2}}{16}=1$$ Heather Z. Numerade Educator ### Problem 68 To prepare for Section$13.2,$review solving quadratic equations (Section$11.1)$Solve for$x$or for$y .
$$\frac{x^{2}}{a^{2}}=1$$

Heather Z.

### Problem 69

To prepare for Section $13.2,$ review solving quadratic equations (Section $11.1)$
Solve for $x$ or for $y . $$\frac{(x-1)^{2}}{25}=1$$ Heather Z. Numerade Educator ### Problem 70 To prepare for Section$13.2,$review solving quadratic equations (Section$11.1)$Solve for$x$or for$y .
$$\frac{(y+5)^{2}}{12}=1$$

Heather Z.

### Problem 71

To prepare for Section $13.2,$ review solving quadratic equations (Section $11.1)$
Solve for $x$ or for $y . $$\frac{1}{4}+\frac{(y+3)^{2}}{36}=1$$ Heather Z. Numerade Educator ### Problem 72 To prepare for Section$13.2,$review solving quadratic equations (Section$11.1)$Solve for$x$or for$y .
$$\frac{1}{9}+\frac{(x-2)^{2}}{4}=1$$

Heather Z.

### Problem 73

On a piece of graph paper, draw a line and a point not on the line. Then plot several points that are the same distance from the point and from the line. What shape do the points appear to form? How is this set of points different from a circle?

Heather Z.

### Problem 74

If an equation has two terms with the same degree, can its graph be a parabola? Why or why not?

Heather Z.

### Problem 75

Find an equation of a circle satisfying the given conditions.
Center $(3,-5)$ and tangent to (touching at one point) the $y$ -axis

Heather Z.

### Problem 76

Find an equation of a circle satisfying the given conditions.
Center $(-7,-4)$ and tangent to the $x$ -axis

Heather Z.

### Problem 77

Find an equation of a circle satisfying the given conditions.
The endpoints of a diameter are $(7,3)$ and $(-1,-3)$

Heather Z.

### Problem 78

Find an equation of a circle satisfying the given conditions.
Center $(-3,5)$ with a circumference of $8 \pi$ units

Heather Z.

### Problem 79

Find an equation of a circle satisfying the given conditions.
Find the point on the $y$ -axis that is equidistant from $(2,10)$ and $(6,2)$

Heather Z.

### Problem 80

Find an equation of a circle satisfying the given conditions.
Find the point on the $x$ -axis that is equidistant from $(-1,3)$ and $(-8,-4)$

Heather Z.

### Problem 81

The equation $x^{2}+y^{2}=\frac{81}{4},$ where $x$ and $y$ represent the number of meters from the center, can be used to draw the outer circle on a wrestling mat used in International, Olympic, and World Championship wrestling. The equation $x^{2}+y^{2}=16$ can be used to draw the inner edge of the red zone. Find the area of the red zone.
( IMAGE CANNOT COPY)

Heather Z.

### Problem 82

Snowboarding. Each side edge of the Burton $X 8$ 155 snowboard is an arc of a circle with a "running length" of $1180 \mathrm{mm}$ and a "sidecut depth" of $23 \mathrm{mm}$
(GRAPH CANNOT COPY)
a) Using the coordinates shown, locate the center of the circle. (Hint: Equate distances.)
b) What radius is used for the edge of the board?

Heather Z.

### Problem 83

The Never Summer Infinity 149 snowboard has a running length of $1160 \mathrm{mm}$ and a sidecut depth of $23.5 \mathrm{mm}$ (see Exercise 82 ). What radius is used for the edge of this snowboard?

Heather Z.

### Problem 84

The Rossignol Blast ski, when lying flat and viewed from above, has edges that are arcs of a circle. (Actually, each edge is made of two arcs of slightly different radii. The arc for the rear half of the ski edge has a slightly larger radius.)
(IMAGE CANNOT COPY)
a) Using the coordinates shown, locate the center of the circle. (Hint: Equate distances.)
b) What radius is used for the arc passing through
$(0,1.5)$ and $(72,0) ?$

Heather Z.

### Problem 85

Ace Carpentry needs to cut ean arch for the top of an entranceway. The arch needs to be 8 ft wide and 2 ft high. To draw the arch, the carpenters will use a stretched string with chalk eattached at an end as a compass.
(IMAGE CANNOT COPY)
a) Using a coordinate system, locate the center of the circle.
b) What radius should the carpenters use to draw the arch?

Heather Z.

### Problem 86

During an archaeological dig, Martina finds the bowl fragment shown below. What was the original diameter of the bowl?
(IMAGE CANNOT COPY)

Heather Z.

### Problem 87

A ferris wheel has a radius of $24.3 \mathrm{ft} .$ Assuming that the center is $30.6 \mathrm{ft}$ off the ground and that the origin is below the center, as in the following figure, find an equation of the circle.
(IMAGE CANNOT COPY)

Heather Z.

### Problem 88

Use a graph of the equation $x=y^{2}-y-6$ to approximate to the nearest tenth the solutions of each of the following equations.
a) $y^{2}-y-6=2$ (Hint: Graph $x=2$ on the same set of axes as the graph of $x=y^{2}-y-6 .$
b) $y^{2}-y-6=-3$

Heather Z.

### Problem 89

Power of a Motor. The horsepower of a certain kind of engine is given by the formula
$$H=\frac{D^{2} N}{2.5}$$
where $N$ is the number of cylinders and $D$ is the diameter, in inches, of each piston. Graph this equation, assuming that $N=6$ (a six-cylinder engine). Let $D$ run from 2.5 to 8

Heather Z.

### Problem 90

If the equation $x^{2}+y^{2}-6 x+2 y-6=0$ is written as $y^{2}+2 y+\left(x^{2}-6 x-6\right)=0,$ it can be regarded as quadratic in $y .$
a) Use the quadratic formula to solve for $y .$
b) Show that the graph of your answer to part (a) coincides with the graph on p. 944

Heather Z.

### Problem 91

How could a graphing calculator best be used to help you sketch the graph of an equation of the form $x=a y^{2}+b y+c ?$

Heather Z.