5­3 Transforming Parabolas Day 1
5.3
November 19, 2008
ing Parabolas ­ Day 1
Objectives: Use the vertex form of a quadratic function to:
graph quadratic functions and
write the equations of quadratic functions from graphs.
Nov 15­7:33 PM
1
5­3 Transforming Parabolas Day 1
November 19, 2008
Nov 15­8:36 PM
2
5­3 Transforming Parabolas Day 1
November 19, 2008
Quadratic Functions
* equation in vertex form f(x) = a(x ­ h)2 + k
* the graph looks like a "U" * a impacts the size
Jun 2 ­ 8:52 AM
3
5­3 Transforming Parabolas Day 1
November 19, 2008
Quadratic Functions
* equation in vertex form f(x) = a(x ­ h)2 + k
* the graph looks like a "U" * a impacts the size
* a>1 makes the graph more narrow
* 0<a<1 makes the graph wider
* a<0 flips upsidedown
Jun 2 ­ 8:52 AM
4
5­3 Transforming Parabolas Day 1
November 19, 2008
Quadratic Functions
* equation in vertex form f(x) = a(x ­ h)2 + k
* the graph looks like a "U" * a impacts the size
* a>1 makes the graph more narrow
* 0<a<1 makes the graph wider
* a<0 flips upsidedown
* h is the horizontal movement * k is the vertical movement
Jun 2 ­ 8:52 AM
5
5­3 Transforming Parabolas Day 1
November 19, 2008
Quadratic Functions
2
* equation in vertex form f(x) = a(x - h) + k
What do changes in "a", "h" & "k" look like when
you graph a quadratic function?
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Jun 2 ­ 10:27 AM
6
5­3 Transforming Parabolas Day 1
November 19, 2008
How do you find points on the graph with different values of a?
Graph the Quadratic Parent Function: y = x2
Re­written: y = 1(x ­ 0)2 + 0
Vertex: (0, 0)
Axis of Symmetry: x = 0
Table of values to graph:
x
y
Graph: y = 2x2 (on the same graph)
What changes are caused by a = 2?
Nov 15­10:02 PM
7
5­3 Transforming Parabolas Day 1
November 19, 2008
How else could you find points on the graph?
Nov 15­8:39 PM
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5­3 Transforming Parabolas Day 1
November 19, 2008
Graph each quadratic function &
find the domain and range:
1. f(x) = (x + 4)2 - 2
-4
D:
R:
2. f(x) = (x - 2)2 - 3
3. f(x) = - (x - 1)2 + 2
4
4
4
2
2
2
-2
2
4
-4
-2
2
4
-4
-2
2
-2
-2
-2
-4
-4
-4
4
D:
R:
D:
R:
Graphs are hiding!!!
Jun 2 ­ 9:10 AM
9
5­3 Transforming Parabolas Day 1
November 19, 2008
Graph each quadratic function &
find the domain and range:
1. f(x) = -(x + 3)2 + 1
2. f(x) = 4(x + 2)2 - 3
4
4
4
4
2
2
2
2
-4
D:
R:
-2
2
4
-4
-2
2
4
3. f(x)= - 1/2(x - 1)2 + 4
4
-- 4
2
-- 2
2
2
-2
-2
2
-- 2
-4
-4
4
-- 4
4
4
D:
R:
D:
R:
Graphs are hiding!!!
Jun 2 ­ 9:10 AM
10
5­3 Transforming Parabolas Day 1
November 19, 2008
Nov 15­8:40 PM
11
5­3 Transforming Parabolas Day 1
November 19, 2008
y = 2(x + 1)2
Nov 15­8:41 PM
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5­3 Transforming Parabolas Day 1
DO
4
U UNDERSTAND??
4
4
2
- 4
- 2
November 19, 2008
2
4
2
4
2
- 2
-4
- 4
-4
2
-4
2
-2
4
-2
-2
2
4
4
-2
-4
-4
-2
-4
2
2
-2
2
4
4
-2
4
2
-4
-2
-4
-4
-2
2
4
-2
-4
Homework:
page 255 (2 - 10, 13 - 20, 24 - 26, 43 - 45, 76, 77)
Jun 2 ­ 10:05 AM
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Attachments
Quadratic slider.gsp