2.1A Using Transformations to Graph Quadratic Functions
Objectives:
F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k).
A.CED.2: Graph equations on coordinate axes with labels and scales.
For the board: You will be able to transform quadratic functions and describe the effects of changes in the
coefficients of y = a(x – h)2 + k.
Bell Work 2.1:
For each translation of (-2, 5), give the coordinates of the translated point.
1. 6 units down
2. 3 units right
For each function, evaluate f(-2), f(0), and f(3).
3. f(x) = 2x + 6
4. f(x) = – 5x + 1
Anticipatory Set:
Linear Parent Graph: f(x) = x
x
-1
0
1
Quadratic Parent Function: f(x) = x2
x
-2
-1
0
1
2
y
-1
0
1
y
4
1
0
1
4
In general, if a function involves adding/subtracting or multiplying a function by a number “outside” the
function, this signals some kind of vertical movement.
Examples: f(x) = 3x2, f(x) = x2 – 5
In general, if a function involves adding/subtracting or multiplying a function by a number “inside” the
function, this signals some kind of horizontal movement.
Examples: f(x) = ( ½ x)2, f(x) = (x + 4)2
Instruction:
Summary of the quadratic transformations using function notation:
f(x) = x2 + 2 translation up 2 units
f(x) = x2 – 2 translation down 2 units
2
f(x) = (x + 2) translation left 2 units
f(x) = (x – 2)2 translation right 2 units
f(x) = -x2
reflect over x-axis
f(x) = (-x)2
f(x) = 2x2
f(x) = ½ x2
vertical stretch, factor of 2
vertical compression, factor of ½
reflect over y-axis
f(x) = (2x)2
f(x) = (½ x)2
horizontal compression, factor of ½
horizontal stretch, factor 2
Open the book to page 60 – 61 and read examples 2 and 3.
Example: Using the graph of f(x) = x2, describe the transformations of each of the following functions
a. g(x) = 3(x – 2)2 – 5.
Vertically stretched by a factor of 3, translated right 2 and down 5.
b. g(x) = [2(x + 5)]2 – 3.
Horizontally compressed by a factor of ½, translated left 5 and down 3.
White Board Activity:
Practice: Using the graph of f(x) = x2, describe the transformations in each of the following functions.
a. f(x) = - ½ (x + 4)2 – 3
Reflected over the x-axis, vertically compressed by a factor of ½,
translated left 4 and down 3
b. f(x) = [-4(x + 1)]2 – 5
Reflected over the y-axis, horizontally compressed by a factor of ¼ ,
Translated left 1 and down 5
Open the book to page 62 and read example 4.
Example: Use the description to write the quadratic function.
The parent function f(x) = x2 is vertically stretched by a factor of 4/3 and then translated
2 units left and 5 units down to create g.
g(x) = 4/3(x + 2)2 – 5
White Board Activity:
Practice: Use the following description to write the quadratic function.
a. The parent function f(x) = x2 is vertically compressed by a factor of 1/3 and translated
2 units right and 4 units down to create g(x).
g(x) = 1/3(x -2)2 - 4
b. The parent function f(x) = x2 is reflected over the x-axis and then translated 5 units left
and 1 unit up to create h(x).
g(x) = -(x + 5)2 + 1
Assessment:
Question student pairs.
Independent Practice:
Text: pg. 64 – 65 prob. 5 – 15, 20 – 30, 33 – 41.
For a Grade:
Text: pg. 64 – 65 prob. 6, 14, 28, 30, 34.