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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

Graph. Be sure to label each vertex.

$$x=-\frac{1}{2} y^{2}$$

Heather Z.

Numerade Educator

Graph. Be sure to label each vertex.

$$y=-\frac{1}{2} x^{2}$$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(0,0),$ radius 6

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(0,0),$ radius 5

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(7,3),$ radius $\sqrt{5}$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(5,6),$ radius $\sqrt{2}$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(-4 \text { 3) radius } 4 \text { ) } \sqrt{3}$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(-2,7),$ radius $2 \sqrt{5}$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(-7,-2),$ radius $5 \sqrt{2}$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(-5,-8),$ radius $3 \sqrt{2}$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(0,0),$ passing through $(-3,4)$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(-4,1),$ passing through $(-2,5)$

Heather Z.

Numerade Educator

Find an equation of the circle satisfying the given conditions.

Center $(-1,-3),$ passing through $(-4,2)$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$x^{2}+y^{2}=64$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$x^{2}+y^{2}=36$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

(x+1)^{2}+(y+3)^{2}=36

$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

(x-2)^{2}+(y+3)^{2}=4

$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

(x-4)^{2}+(y+3)^{2}=10

$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

(x+5)^{2}+(y-1)^{2}=15

$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$x^{2}+y^{2}=10$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$x^{2}+y^{2}=7$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$(x-5)^{2}+y^{2}=\frac{1}{4}$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

x^{2}+(y-1)^{2}=\frac{1}{25}

$$

Heather Z.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

x^{2}+y^{2}+10 y-75=0

$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

x^{2}+y^{2}-8 x-84=0

$$

Heather Z.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

36 x^{2}+36 y^{2}=1

$$

Heather Z.

Numerade Educator

Find the center and the radius of each circle. Then graph the circle.

$$

4 x^{2}+4 y^{2}=1

$$

Heather Z.

Numerade Educator

Graph using a graphing calculator.

$$x^{2}+y^{2}+14 x-16 y+54=0$$

Heather Z.

Numerade Educator

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

Heather Z.

Numerade Educator

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

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.

Numerade Educator

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

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.

Numerade Educator

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

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.

Numerade Educator

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.

Numerade Educator

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

Heather Z.

Numerade Educator

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.

Numerade Educator

Find an equation of a circle satisfying the given conditions.

Center $(-7,-4)$ and tangent to the $x$ -axis

Heather Z.

Numerade Educator

Find an equation of a circle satisfying the given conditions.

The endpoints of a diameter are $(7,3)$ and $(-1,-3)$

Heather Z.

Numerade Educator

Find an equation of a circle satisfying the given conditions.

Center $(-3,5)$ with a circumference of $8 \pi$ units

Heather Z.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

During an archaeological dig, Martina finds the bowl fragment shown below. What was the original diameter of the bowl?

(IMAGE CANNOT COPY)

Heather Z.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

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.

Numerade Educator

Why should a graphing calculator's window be "squared" before graphing a circle?

Heather Z.

Numerade Educator