I. Reflections

_________________________________

are like mirror images as seen across a

line or a point

1. Reflect the shape over the x-axis.

2. Reflect over the line x = 1

3. Reflect over the line y=-x

II. Dilations

A __________________________________

is a transformation which changes the size

of a figure but not its shape. This reduces

or enlarges the figure to a similar figure.

1. Dilation of 1.5

2. Dilation of 2

3. Write a rule to describe the following

dilation S(1, 4), X(0, 5), F(5, 4), E(1, 2) to

E’(0.5, 1), X’(0, 2.5), S’(0.5, 2), F’(2.5, 2)

III. Transformations

A ________________________________

occurs when a figure is moved by sliding it

up, down, left or right

1. Graph and connect the points (2, 2), (3,

4), (4, 2) and (5, 4), then translate the

points along the vector <2, -2>

2. Translate along the vector: < −4, −3 >

3. Translate the image (x+4, y-1)

IV. Rotations

_____________________________- a point

around which a figure is rotated

_____________________________- which

way a figure is rotated.

a. When a figure is rotated 90°

counterclockwise about the origin,

multiply the y-coordinate by -1 and

switch the x- and y- coordinates.

(x, y) _____________

b. When a figure is rotated 180° about the

origin, multiply both coordinates by -1.

(x, y) _____________

c. When a figure is rotated 270°

counterclockwise (90° clockwise)

about the origin, multiply the x-

coordinate by -1, then switch the x- & y-

coordinates.

(x, y) _____________

1. Rotation 180° about the origin

2. Rotation 180° about the origin 𝑍(1, −3), 𝐾(8, 1), 𝐶(0, −6), 𝑁(10, −4)

________________________________

3. Rotation 90° clockwise about the origin

4. Rotation 90° counterclockwise about

the origin 𝑍(1, −3), 𝐾(8, 1), 𝐶(0, −6), 𝑁(10, −4)

_________________________________

V. Composition of Transformations

The _________________ of

transformations is one, two, or more

transformations.

1. Quadrilateral BGTS has vertices B(–3, 4),

G(–1, 3), T(–1 , 1), and S(–4, 2). Graph

BGTS and its image after a translation

along <5, 0> and a reflection in the x-

axis.

2. ΔTUV has vertices T(2, –1), U(5, –2), and

V(3, –4). Graph ΔTUV and its image after

a translation along <–1 , 5> and a

rotation 180° about the origin.

3. Pre-image: H(2,2), I(-2,2), J(-2,-2),

K(2,-2)

Rotate the figure

180°

𝐻𝐼( , ), 𝐼𝐼( ,

), 𝐽𝐼( , ), 𝐾𝐼( ,

)

Translate the

figure according

to (x,y)→(x+2,y+2)

𝐻𝐼( , ), 𝐼𝐼( ,

), 𝐽𝐼( , ), 𝐾𝐼( ,

)

Reflect the figure

over the line y = x

𝐻𝐼( , ), 𝐼𝐼( ,

), 𝐽𝐼( , ), 𝐾𝐼( ,

)

Practice Test:

1. ∆𝐴𝐵𝐶 is transformed into ∆𝐷𝐸𝐹. What

transformation was performed to make ∆𝐷𝐸𝐹

A. Reflect ∆𝐴𝐵𝐶 across the x-axis, then

translate it 2 units up.

B. Reflect ∆𝐴𝐵𝐶 across the x-axis, then

translate it 2 units down.

C. Rotate ∆𝐴𝐵𝐶 90° clockwise about the

origin, then translate it 2 units up.

D. Rotate ∆𝐴𝐵𝐶 90° clockwise about the

origin, then translate it 2 units down.

2. Triangle ABC has vertices A(1, 2), B(3, 5),

and C(4, 3). Using the origin as a center

of dilation, triangle ABC is dilated by a

scale factor of 3 to create triangle

A’B’C’. Which statement can be used to justify that triangle ABC is similar to

triangle A’B’C’?

A. 𝐴𝐵̅̅ ̅̅ = 𝐴′𝐵′̅̅ ̅̅ ̅̅ and 𝐵𝐶̅̅ ̅̅ = 𝐵′𝐶′̅̅ ̅̅ ̅̅

B. ∠𝐴 ≅ ∠𝐴′ and ∠𝐵 ≅ ∠𝐵′ C. The sum of the angles of each triangle

remains 180 degrees.

D. The area of triangle A’B’C’ is 3 times of triangle ABC.

3. If ∆𝑅𝑆𝑇 is the result of two

transformations on ∆𝑁𝑃𝑄, which two of

these statemtns can be combined to

prove that ∆𝑅𝑆𝑇~∆𝑁𝑃𝑄?

Statement 1: ∠𝑄 ≅ ∠𝑇

Statement 2: ∠𝑁 ≅ ∠𝑅

Statement 3: 𝑆𝑇𝑃𝑄 = 𝑅𝑆𝑁𝑃

Statement 4: 𝑅𝑆 = 34 𝑁𝑃

A. Statement 1 and 2

B. Statement 1 and 4

C. Statement 2 and 3

D. Statement 3 and 4

4. Which of the following transformations

maps Figure A onto Figure B?

A. Translate Figure A 3 units right and 2

units down.

B. Translate Figure A 3 units right, and

then reflect it across the x-axis.

C. Reflect Figure A across the x-axis, and

then translate it 3 units left.

D. Reflect Figure A across the u-axis, and

then translate it 3 units right.

5. If 𝑀𝑁̅̅ ̅̅ ̅ is mapped to 𝑃𝑄̅̅ ̅̅ , which combination

of transformations could NOT have taken

place?

A. Line segment MN was reflected over the x-

axis and then reflected over the y-axis.

B. Line segment MN was translated 10 units to

the right and then reflected over the x-axis.

C. Line segment MN was rotated 180° clockwise about Point N and then

translated 10 units to the right.

D. Line segment MN was reflected over the y-

axis and then rotated 90° counterclockwise

about Point N.

6. Triangle EGF is graphed below.

Triangle EGF will be rotated 90°

counterclockwise around the origin and will

then be reflected across the y-axis, producing

an image triangle. Which additional

transformation will map the image triangle back

onto the original triangle?

A. Rotate 270° counterclockwise around the

origin

B. Rotate 180° counterclockwise around the

origin

C. Reflect across the line y=-x

D. Reflect across the line y=x

7. Which set of transformations will map

Figure STUVW onto Figure MNPQR?

A. A reflection across the y-axis, and then a

reflection across the x-axis

B. A translation of 10 units down, and then

reflection across y-axis

C. A 90° counterclockwise rotation about the

origin, and then a reflection across the y-

axis

D. A 90° counterclockwise rotation about the

origin, and then a reflection across the x-

axis

8. Jose created a tessellation for a carpet

design shown below.

He produced the following pattern.

Which transformations did he use to create the

pattern?

A. Rotations and Reflections

B. Rotations and Translations

C. Reflections and Translations

D. Reflections, Rotations, and Translations

9. What transformations have occurred to

create the function 𝑓(𝑥) = 3𝑥3 − 4 from

the function (𝑔) = 𝑥3

A. The graph of the function has been

stretched horizontally and shifted up four

units.

B. The graph of the function has been

stretched vertically and shifted up four

units.

C. The graph of the function has been

stretched horizontally and shifted down

four units

D. The graph of the function has been

stretched vertically and shifted down four

units.

10. If the graph of 𝑓(𝑥) = √𝑥 + 3 is translated

2 units right and 4 units down, which of

these functions describes the

transformation graph?

A. 𝑔(𝑥) = √𝑥 − 2 − 1

B. 𝑔(𝑥) = √𝑥 + 2 − 1

C. 𝑔(𝑥) = √𝑥 − 2 + 7

D. 𝑔(𝑥) = √𝑥 + 2 + 7

Unit 2-Review- (parallel lines and transversals, congruent triangles, midsegents)

1. Identify each set of angles below as corresponding, vertical, alternate interior, alternate exterior, consecutive or

linear pair. (use the figure to the right to answer a-h)

a. _______________________________

b. _______________________________

c. _______________________________

d. _______________________________

e. _______________________________

f. _______________________________

g. _______________________________

h. _______________________________

Solve for the missing angle value given: (use the figure to the right o answer a-f)

a. b. c. d. e. f.

Solve for the missing variable and the missing angle values that are indicated (#4-7)

2. 5.

Equation:________________________ Equation:_____________________________

X=_____ X=_______

Fill in the following proof (#8-9)

8. Given the diagram below, prove that x=5

Statement Reason

1. 23x-5=21x+5

2. Subtraction Property

3. 2x-5=5

4. Addition Property

5. 2x=10

6.

7. x=5

Solve for the indicated values (#10-14)

10. 11. 12.

x=__________ x=__________ 13. 14.

a=_______ b=______ c=______

d=______ f=______

Determine the distance or midpoint of the following line segments (#15-17)

15. (4, 6) (1,5) Distance:___________________ Midpoint:___________________

16. (7, -5) (9, -1) Distance:___________________ Midpoint:___________________

17. AB=___________

BC=___________

AC=___________

Perimeter of =_________________

Determine if the following figures are congruent, if they are give a congruence statement and why the two shapes are

congruent. a. Are the triangles congruent b. Give a congruence statement c. Why are the triangles

congruent

18. 19. 20. 21.

a. __________________ a. __________________ a. __________________ a.__________________

b. __________________ b. __________________ b. __________________ b. _________________

c. __________________ c. __________________ c. __________________ c. _________________

B

A C

D

B

D C A

E

L

O

N

M

Z

Y

X

W

D

X

Unit 3 - Trigonometry Review Name:

*For trig functions make sure your calculator is in _______________________________ mode.

Trig Function Sides

Sin

Cos

Tan

• The __________________________ should always be with the trig function

o In some cases you won’t know the angle, so the variable, usually _________________________, will be

with the trig function

Find the value of each trigonometric ratio

__________________________ ______________________________ ______________________________

1. Find the length of the missing side. Round your answer to the nearest tenth.

• Trying to find the ________________

• Know the _________________________

• Use:

2. Find the length of the missing side. Round your answer to the nearest tenth.

• Trying to find the ________________

• Know the _________________________

• Use:

3. Find the length of the missing side. Round your answer to the nearest tenth.

• Trying to find the ________________

• Know the _________________________

• Use:

4. Find the length of the missing side. Round your answer to the nearest tenth.

• Trying to find the ________________

• Know the _________________________

• Use:

5. Find the missing angle. Round your answer to the nearest degree.

Know the _______________________ and the _________________________

Use:

6. A flagpole casts a 100 foot shadow. From the ground to the top of the flagpole you measure an angle

of How high is the flagpole?

Trying to find the ________________

Know the _________________________

Use:

Pythagorean Theorem Review

The Pythagorean Theorem can be used in any _____________________________ triangle where you know two

_____________________, and are trying to find another side

o Unlike the trig functions above, you use the Pythagorean Theorem when you don’t know or aren’t trying to find angles

o Pythagorean Theorem ___________________________________________________

a and b represents the _____________________________________

c represents the _____________________________________________

Find the missing side in each right triangle below:

4. The size of a television screen is given by the length of the diagonal of the screen. What size is a television

screen that is 21.6 inches wide and 16.2 inches high?

5. The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the

ladder is leaned against the wall, what is the distance above the ground it will reach?

30-60-90 Right Triangles:

● The ____________________________ of all right triangles are opposite of the

____________________________angle.

● Short leg is opposite of the ___________________________ angle

● Longest leg is opposite of the __________________________side.

● Always start with short leg:

Long Leg=____________________________________

Hypotenuse=__________________________________

Examples: Solve for the missing side values

1. 2.

x=________ m=________

y=________ n=________

3. 4.

x=________ x=________

y=________ y=________

45-45-90 Right Triangles:

● The ____________________________ of all right triangles are opposite of the

____________________________angle.

Because we are working with 45-45-90 Triangle, we know that because of the two congruent angles, the legs will

be _______________ creating a right isosceles triangle.

Leg:____________________________________

Hypotenuse:_____________________________

Examples: Solve for the missing side values

1. 2.

x=________ x=________

y=________ y=________

3. 4.

m=________ a=________

n=________ b=________

Unit 4 - Graphing Quadratics Name:

For each quadratic equation below, describe the transformation and identify the vertex, range, and

intervals of increase/decrease:

1. f(x) = 4(x – 2)2 – 9

____________________________________________________

____________________________________________________

Vertex = __________________________Max or Min

Range = _________________________________________

Increase = _______________________________________

Decrease = ______________________________________

2. y = ½(x +4)2 – 3

____________________________________________________

____________________________________________________

Vertex = __________________________Max or Min

Range = _________________________________________

Increase = _______________________________________

Decrease = ______________________________________

3. f(x) = –3(x – 3)2 + 8

____________________________________________________

____________________________________________________

Vertex = __________________________Max or Min

Range = _________________________________________

Increase = _______________________________________

Decrease = ______________________________________

4. f(x) = –1/4(x – 1)2

____________________________________________________

____________________________________________________

Vertex = __________________________Max or Min

Range = _________________________________________

Increase = _______________________________________

Decrease = ______________________________________

5. y = x2 + 4

____________________________________________________

____________________________________________________

Vertex = __________________________Max or Min

Range = _________________________________________

Increase = _______________________________________

Decrease = ______________________________________

6. y = 2(x + 7)2

____________________________________________________

____________________________________________________

Vertex = __________________________Max or Min

Range = _________________________________________

Increase = _______________________________________

Decrease = ______________________________________

Classwork/Homework – Quadratic Review Name:

Find all the key features of the quadratic functions listed below. Remember, if your equation is in standard

form ( you will need to use the equation to find your axis of symmetry/vertex. If the

equation is in vertex form your vertex is the point .

1.

Axis of Symmetry: _________________________________

Vertex: ______________________________________________

Y-Intercept: ________________________________________

X-Intercept(s); _____________________________________

Domain: ____________________________________________

Range: ______________________________________________

Increase: ___________________________________________

Decrease: __________________________________________

2.

Transformation: ___________________________________

______________________________________________________

Axis of Symmetry: _________________________________

Vertex: ______________________________________________

Y-Intercept: ________________________________________

X-Intercept(s); _____________________________________

Domain: ____________________________________________

Range: ______________________________________________

Increase: ___________________________________________

Decrease: __________________________________________

Unit 5 - Radicals

Simplify the following expressions under the radical.

1) √ 2) √ 3) √ 4) √

5) √ 6) √ 7) √ 8) 2√

Changing Forms – Radical to Exponent/Exponent to Radical

Rewrite each of the following in exponential form.

1. (√ ) 2. (√ ) 3. ( √ )

Rewrite each of the following in radical form.

4. 5.( ) 6. ( )

Unit 6 – Solving Quadratics Name:

Recall A quadratic function/equation is a function were the highest exponent is ______________________

There are two main things that you will be asked to do with quadratic functions

1. ______________________________________ 2. ______________________________________

For both factoring and solving, make sure your equation is in the form ____________________________________

Factoring Quadratic Functions

Basic Factoring Equations in the form

Where there is no number in front of the leading

coefficient (x2), factoring by finding two

numbers that multiply to _____ that also add up to

_______

Before, we drew a factoring triangle to help

1.

2. 3.

Factoring with a GCF Equations in the form

the leading coefficient or a is a common factor

Divide each term by a, and leave a in front of

your factored form

Once you’ve divide by a, follow the basic factoring steps

4.

5. 6.

Factoring with no GCF Equations in the form

the leading coefficient or a is not a GCF

Multiply a and c then rewrite your equation

Follow the steps from the basic factoring, but to

undo multiplying by a, divide both factoring by a

o If the fraction simplifies, simplify it. If it doesn’t slide the denominator in front of x in your factor.

7.

8. 9.

Solving Quadratic Equations using the Quadratic Formula

When solving quadratic equations, the quadratic formula works for all quadratics

o Always make sure your equation is in the form ___________________________________________________

Recall the quadratic formula:

1.

2.

3.

4.

5.