Algebra 2
7.5 DAY 1
Graphing Square Root Functions
Graphing Cube Root Functions
Transformations
Algebra 2 7.5 Notes
Graphing Square Root and Cube Root Functions
Functions you should know [Called Parent Functions!]
Opens: if a is +, parabola opens up
if a is ­, parabola opens down
(h,k)
Absolute Value Function
Opens: if a is +, abs. value opens up
if a is ­, abs. value opens down
(h,k)
(h,k)
(h,k)
(h,k)
Graph the absolute value functions. Give the Vertex (V).
Write the transformations.
Transformations:
Transformations:
Transformations:
1________________
1________________
1________________
2________________
2________________
2________________
Graph the quadratic Functions. Identify the Vertex(V), Axis of Symmetry (AOS),
and the direction the parabola opens (up or down). Then state the transformations:
V:________
Opens:_____
V:________
Opens:_____
V:________
Opens:_____
Transformations:
Transformations:
Transformations:
1________________
1________________
1________________
2________________
2________________
2________________
V:________
Opens:_____
V:________
Opens:_____
V:________
Opens:_____
Transformations:
Transformations:
Transformations:
1________________
1________________
1________________
2________________
2________________
2________________
3_______________
3_______________
3_______________
Transformations
y = a(x­h)2 + k
y =a x­h + k
We will do the transformations in the same order
every time (left/right, up/down, flip over x­axis))
]
y = a(x­h)2 + k
y =a x­h + k
y = a(x­h)2 + k
]
3
horizontal shift left or right
y =a x­h + k
vertical shift up or down
y = a(x­h)2 + k
]
if "a" is negative , the graph is flipped
(reflected) over the x­axis
Given the function y=x2, perform the following transformations and draw the new function
1. right 2, down 3
3. right 1, up 4, flip over the x­axis
2. left 1, up 1
Given the function y= x, perform the following transformations and draw the new function
1. right 2, down 3
3. up 2, flip over the x­axis
2. left 1, up 1
4. right 1, up 2,
5. left 2, down 1, flip over the x­axis flip over the x­axis
3
Given the function y= x, perform the following transformations and draw the new function
1. right 2, down 3
2. left 1, up 1
3. up 2, flip over the x­axis
4. left 2, up 3,
5. right 1, down 2, flip over the x­axis flip over the x­axis
Algebra 2
7.5 DAY 2
Graphing Square Root Functions
Graphing Cube Root Functions
Transformations
Algebra 2 7.5 Notes DAY 2 Transformations of Functions
Describe how to obtain the following graphs from y=x2
1.
1 2.
1
Vertex:_______
Vertex:_______
Transformations:
Transformations:
3
3. 4. 5.
Vertex:_______
Vertex:_______
Vertex:_______
Transformations:
Transformations:
Transformations:
Describe how to obtain the following graphs from y=
x+3
6.
+2 + 1 7.
Start Dot:_______
Start Dot:_______
Transformations:
Transformations:
x
Describe how to obtain the following graphs from y=
8. 9. Start Dot:_______
Start Dot:_______
Transformations:
Transformations:
x
1
3
Describe how to obtain the following graphs from y= x
10. 11. x+2 + 1
x
Center Dot:_______
Center Dot:_______
Transformations:
Transformations:
12. 13. x­2
x+1 ­ 2
Center Dot:_______
Center Dot:_______
Transformations:
Transformations:
Algebra 2 7.5
DAY 1 Notes completed
Graphing Square Root Functions
Graphing Cube Root Functions
Transformations
Algebra 2 7.5 Notes
Graphing Square Root and Cube Root Functions
Functions you should know [Called Parent Functions!]
Opens: if a is +, parabola opens up
if a is ­, parabola opens down
Absolute Value Function
Opens: if a is +, abs. value opens up
if a is ­, abs. value opens down
Graph the absolute value functions. Give the Vertex (V).
Write the transformations.
Vertex
Dot
Transformations:
Transformations:
Transformations:
1________________
1________________
1________________
2________________
2________________
2________________
Graph the quadratic Functions. Identify the Vertex(V), Axis of Symmetry (AOS),
and the direction the parabola opens (up or down). Then state the transformations:
Vertex
Dot
V:________
Opens:_____
V:________
Opens:_____
V:________
Opens:_____
Transformations:
Transformations:
Transformations:
1________________
1________________
2________________
2________________
1________________
2________________
2________________
V:________
Opens:_____
V:________
Opens:_____
V:________
Opens:_____
Transformations:
Transformations:
Transformations:
1________________
1________________
1________________
2________________
2________________
2________________
3_______________
3_______________
3_______________
2________________
Transformations
y = a(x­h)2 + k
y =a x­h + k
We will do the transformations in the same order
every time (left/right, up/down, flip over x­axis))
]
y = a(x­h)2 + k
y =a x­h + k
y = a(x­h)2 + k
]
3
horizontal shift left or right
y =a x­h + k
vertical shift up or down
y = a(x­h)2 + k
]
if "a" is negative, the graph is flipped
(reflected) over the x­axis
Given the function y=x2, perform the following transformations and draw the new function
1. right 2, down 3
3. right 1, up 4, flip over the x­axis
2. left 1, up 1
Given the function y= x, perform the following transformations and draw the new function
1. right 2, down 3
2. left 1, up 1
Start
Dot
3. up 2, flip over the x­axis
4. right 1, up 2,
5. left 2, down 1, flip over the x­axis flip over the x­axis
3
Given the function y= x, perform the following transformations and draw the new function
1. right 2, down 3
2. left 1, up 1
Center
Dot
3. up 2, flip over the x­axis
4. left 2, up 3,
5. right 1, down 2, flip over the x­axis flip over the x­axis
Algebra 2 7.5
DAY 2 Notes completed
Graphing Square Root Functions
Graphing Cube Root Functions
Transformations
Algebra 2 7.5 Notes DAY 2 Transformations of Functions
Describe how to obtain the following graphs from y=x2
1.
1 2.
1
(2,1)
Vertex:_______
(­1,3)
Vertex:_______
Transformations:
Transformations:
1. Right 2
2. Up 1
1. Left 1
2. Up 3
3. Flip (Reflect)
over the
x­axis
3
3. 4. 5.
(0,­4)
(0,0)
(­3,4)
Vertex:_______
Vertex:_______
Vertex:_______
Transformations:
1. Left 3
2. Up 4
Transformations:
1. Flip (Reflect)
over the x­axis
Transformations:
1. Down 4
Describe how to obtain the following graphs from y=
x+3
6.
+2 + 1 7.
(­2,1)
Start Dot:_______
(­3,0)
Start Dot:_______
Transformations:
Transformations:
1. Left 2
2. Up 1
1. Left 3
2. Flip (Reflect)
over the
x­axis
x
Describe how to obtain the following graphs from y=
x
8. 9. 1
(­3,­1)
(0,2)
Start Dot:_______
Start Dot:_______
Transformations:
1. Up 2
2. Flip (Reflect)
over the
x­axis
Transformations:
1. Left 3
2. Down 1
3
Describe how to obtain the following graphs from y= x
10. 11. x+2 + 1
x
(0,0)
(­2,1)
Center Dot:_______
Center Dot:_______
Transformations:
Transformations:
None
1. Up 2
2. Flip (Reflect)
over the
x­axis
12. 13. x­2
x+1 ­ 2
(2,0)
(­1,­2)
Center Dot:_______
Center Dot:_______
Transformations:
1. Right 2
Transformations:
1. Left 1
2. Down 2
3. Flip (Reflect)
over the
x­axis

Function Transformations

Use the diagram to complete the statement. (Figure ABCD → EFGD

P(x)

CIRCLES AND ELLIPSES REVIEW PROBLEMS

Overview of the interpreter

1.6 Determine a Quadratic Equation Given its Roots

Unit F Part 1 Day 2 Domain and Range of Quadratic Functions

Class Plan 3

2.3 Graphing Lines

Analysis of Algorithms

2012 How to Read the Report Card

Global Quantum Dot Solar Cell Market