Name
LESSON
5-1
Date
Class
Reteach
Using Transformations to Graph Quadratic Functions
The graph of a quadratic function is a parabola. A parabola is a curve shaped like the letter U.
2
f x a x h k a 0 Quadratic function
You can make a table to graph a quadratic function.
2
Graph f x x 4x 3.
x
2
f x ⴝ x ⴚ 4x ⴙ 3
0
f 0 0 4 0 3 3
x, f x 0, 3 1
f 1 1 2 4 1 3 0
1, 0 2
f 2 2 4 2 3 1
2, 1 3
f 3 3 4 3 3 0
3, 0 4
f 4 4 4 4 3 3
4, 3 2
2
2
2
Y
Plot the ordered pairs from the table.
Sketch a smooth curve to connect the points.
X
The curve changes at
(2, 1). This point is the
vertex of the function.
Complete the table. Use the ordered pairs to sketch the graph.
1. f x x 2 6x 7
x
f x x 2 6x 7
1
f 1 1 2 6 1 7 1
x, f x 1, 2 2
2, 1 2
f 2 3
f 3 2
3, 2 4
f 4 1
4, 1 5
f5 2
5, 2 Y
X
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-1_rt.indd 6
6
Holt Algebra 2
12/15/05 4:36:01 PM
Process Black
Name
LESSON
5-1
Date
Class
Reteach
Using Transformations to Graph Quadratic Functions
(continued)
Use the graph of f x x 2 as a guide to graph transformations of quadratic functions.
2
Horizontal and vertical translations change the vertex of f x x .
Parent Function
Transformation
The translation shifts f x x 2 :
f x x 2
g x x h 2 k
Vertex: 0, 0 Vertex: h, k h units right h 0 or left h 0 and
k units up k 0 or down k 0 .
The vertex of g x x 4 2 2
is 4, 2 .
2
The graph of f x x is shifted
Y
4 units right and 2 units down.
F X X X
G X X
2
Use the graph of f x x as a guide. Find the vertex of
each translation. Graph each function and then describe the
transformation.
2. g x x 1 2 3
Vertex: 1,
3. h x x 3 2 2
3 Y
Y
X
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
X
Graph is shifted 3 units right and
2 units up.
Graph is shifted 1 unit left and
3 units down.
a207c05-1_rt.indd 7
(3, 2)
Vertex:
7
Holt Algebra 2
12/15/05 4:36:04 PM
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