Download 1. 3 apples + 5 apples = 8 apples 2. 7 halves – 3 halves = 4 halves

Ch 5 Activity Sheets Alg 2 L1 Key
Name _______________________
Algebra 1 Review: SIMPLIFYING Addition vs. Multiplication and Mixing It Up
A) Addition (Subtraction = add the opposite of)
B) Multiplication
(Division = multiply by the reciprocal)
You can add (or subtract) like things, terms.
The “things” don’t change, you simply count up
the number of “things” that you have.
1.
2.
3 apples + 5 apples = 8 apples
7 halves – 3 halves = 4 halves
When multiplying variables, you count up the
number of factors. You write the number of
factors as an exponent. The multiplication
symbols are not always written.
1. x x  x 2
2. 3x 5x  15x 2
7 3 4
  2
3.
2 2 2
3.
4. 3x  7 x  5x  1x
 
2
3
4. 4 x 3x  12x
2
2
2
2
5. 5 x  2 x  4 x  3x
6.
 2 x  3x 5x   30x3
5. 10x  2x 
 2 y  3   7  5 y   2 y  5 y  3  7
3 y  4
7.
 4x
2
 3x    7 x 2  5 x   2 
6.
10 x
 5
2x
6 1
6 x2


2
12 2
12 x
4 x 2  3x  7 x 2  5 x  2
3x 2  8 x  2
8.
x
2
Mixing It Up
The Distributive Property of Multiplication Over
Addition
 2 x  5   3x2  4 x  1 
a  b  c   ab  ac or  b  c  a  ab  ac
x  3x  2 x  4 x  5  1
2
2
The Distributive Property of Multiplication Over
Subtraction
2 x 2  6 x  4
a  b  c   ab  ac or  b  c  a  ab  ac
C) Addition and Multiplication Combined (Remember the Order of Operations!!)

1. 3  2 x  7   3 2x  7 3  6x  21
2.
x
2
 5 x   2   2 x 2  10 x
5. 2  y  5  3  4  7 y  
3. 4 x  5  3x   20 x  12 x write 12 x  20 x
2
S. Stirling Spring 2017

2
2
4. 4 2 x  x  11  8 x  4 x  44
2
2 y  10  12  21 y
23 y  2
Page 1 of 5
Ch 5 Activity Sheets Alg 2 L1 Key
Name _______________________
C) Addition and Multiplication Combined (Cont.) SHOW THE DISTRIBUTIVE PROPERTY!!
Example: There is a reason why we are doing it this way, so follow the example closely!
 x  2  x  7 
x  x  2   7  x  2 
distribute the first factor
x 2  2 x  7 x  14 distribute again
x 2  5 x  14 combine like terms
6.
 3x  5x  2 
5 x  3 x   2  3 x 
8.
 x  3 x  4 
x  x  3  4  x  3
x 2  3x  4 x  12
15 x 2  6 x
x 2  7 x  12
7.
 x  2 x  5 
x  x  2  5  x  2
x 2  2 x  5 x  10
 2 x  5 x  3 
x  2 x  5  3  2 x  5
x 2  7 x  10
2 x 2  5 x  6 x  15
9.
2 x 2  x  15
S. Stirling Spring 2017
Page 2 of 5
Ch 5 Activity Sheets Alg 2 L1 Key
Name _______________________
Ch 5.3 Transforming Parabolas Activity Sheets
Reviewing Transformations (with absolute value)
The absolute value
parent function
f ( x)  x
The vertex is at (0, 0).
Symmetry in the y-values.
V-shaped graph made up
of two linear.
x
y
–2
–1
0
1
2
2
1
0
1
2
Look at the symmetry
y
about the y-axis!

Look at
the slope
of the
left side.
Look at
the slope
of the
x right side.


m  1







m 1

Summary Shifting
Parent Function:
 Shrink or Flip
Summary Stretch,
y x
Parent Function:
y x

Vertical Translations
Translate up k units:
y  x k
Translate down k units:
y  x k
Vertical Stretch |a| > 1
Stretch away from x-axis by a factor of a.
Vertical Shrink (fraction of) 0 < |a| < 1
Shrink toward x-axis by a factor of a.
Horizontal Translations (counter intuitive)
y  xh
Translate right h units:
Reflection in x-axis (negative) a < 0
Reflects over the x-axis and stretches or shrinks.
y  xh
Translate left h units:
ya x
Graph the following using your previous knowledge of transformations. State the transformation made
(ie. Stretch by a factor of 2, or shifted left 5, or flipped vertically…)
1. Shifting:
g ( x)  x  1  3
h( x )  x  5  6
j ( x)  x  2  4
The graph shifts left 5
and down 6.
The graph shifts right
1and up 3.
y
The graph shifts right 2
and up 4.
y
y









x






x







x

















S. Stirling Spring 2017


Page 3 of 5

Ch 5 Activity Sheets Alg 2 L1 Key
Name _______________________
2. Stretch, Shrink and Flip:
h( x ) 
g ( x)  2 x
1
x
2
k ( x)  5 x
Shrink down by a factor of 2. Flip over x-axis & Stretch
down by a factor of 5.
Stretch up factor of 2.
y
y
y









x






x







x




















3. Combined Transformations:
h( x ) 
g ( x)  2 x  3  4
y


x








x











k ( x)  
y



x



j ( x)  3 x  5

y
Stretch up
factor of 2.
Shift right 3
& down 4.


1
x2 5
3





Stretch up by
a factor of 3.
Flip over xaxis.
Shift left 5.


1
x 3 5
4
y



x












S. Stirling Spring 2017

Shrink down
by a factor of
3.
Shift left 2 &
up 5.



Shrink down
by a factor of
4.
Flip over xaxis.
Shift left 3 &
down 5.
Page 4 of 5
Ch 5 Activity Sheets Alg 2 L1 Key
Name _______________________
Introduction: Graphing Quadratic Functions by Transformations
Look at the
symmetry
about they
y-axis!
Parent
The quadratic parent
function
x
–3
–2
–1
0
1
2
3
f ( x)  x 2
The vertex is at (0, 0).
Symmetry in the y-values.
U-shaped graph.

y1
9
4
1
0
1
4
9


Look at
point
symmetry.

Look at
point
symmetry.





x






From the vertex you move over left and right 1, then up 1. From the vertex you move over left and right
2, then up 4. From the vertex you move over left and right 3, then up 9.

Try to use transformations to graph the following. Use tracing paper if you need to.
g ( x)   x  1  3
h( x)   x  5  6
2

y






   












y



x
   


j ( x)  2 x 2
y

x


2






x
   






1
m( x )  x 2
2

y


 
y


x


   
x



x




S. Stirling Spring
2017

2


   

p( x)  
y x  4  1
n( x)    x  3  5
2




   



















Page 5 of 5

