Transformations of Quadratic Functions - Big Ideas Math
Name _________________________________________________________ Date _________
Transformations of Quadratic Functions
2.1
For use with Exploration 2.1
Essential Question How do the constants a, h, and k affect the graph of the quadratic function g ( x ) = a ( x − h ) + k ? 2
1
EXPLORATION: Identifying Graphs of Quadratic Functions Work with a partner. Match each quadratic function with its graph. Explain your reasoning. Then use a graphing calculator to verify that your answer is correct. a. g ( x ) = − ( x − 2)
2
2
4
−6
c. g ( x ) = − ( x + 2) − 2
e. g ( x ) = 2( x − 2)
f. g ( x ) = − ( x + 2) + 2
2
d. g ( x ) = 0.5( x − 2) − 2
A.
b. g ( x ) = ( x − 2) + 2
2
2
4
B.
6
−6
−4
−6
4
D. 6
−6
−4
−6
24
Algebra 2 Student Journal
4
F.
6
−4
6
−4
4
E.
6
−4
4
C.
2
−6
6
−4
Copyright © Big Ideas Learning, LLC All rights reserved.
Name_________________________________________________________
2.1
Date __________
Transformations of Quadratic Functions (continued)
Communicate Your Answer 2. How do the constants a, h, and k affect the graph of the quadratic function
g ( x) = a( x − h) + k ? 2
3. Write the equation of the quadratic function whose graph is shown. Explain your
reasoning. Then use a graphing calculator to verify that your equation is correct. 4
−6
6
−4
Copyright © Big Ideas Learning, LLC All rights reserved.
Algebra 2 Student Journal
25
Name _________________________________________________________ Date _________
Notetaking with Vocabulary
2.1
For use after Lesson 2.1
In your own words, write the meaning of each vocabulary term.
quadratic function
parabola
vertex of a parabola
vertex form
Core Concepts Horizontal Translations
Vertical Translations f ( x) = x 2
f ( x) = x 2 f ( x − h) = ( x − h) y = (x − h)2, h0
x2 y = (x − h)2, h>0
y = x 2 + k, k 0
•
shifts up when k > 0
Notes:
26
Algebra 2 Student Journal
Copyright © Big Ideas Learning, LLC All rights reserved.
Name_________________________________________________________
2.1
Date __________
Notetaking with Vocabulary (continued) Reflections in the x-Axis
f ( x) = x
Reflections in the y-Axis
f ( x) = x 2
2
− f ( x) = − ( x 2 ) = − x 2
f ( − x) = ( − x) = x 2 2
y
y = x2
y
x
x
y = – x2
flips over the x-axis Horizontal Stretches and Shrinks
f ( x) = x
y
y = x 2 is its own reflection in the y-axis. Vertical Stretches and Shrinks
f ( x) = x 2
2
f ( ax) = ( ax) y = (ax)2, a>1
y = x2
y=
a • f ( x) = ax 2
2
x2
y = (ax)2, 0
Transformations of Quadratic Functions
2.1
For use with Exploration 2.1
Essential Question How do the constants a, h, and k affect the graph of the quadratic function g ( x ) = a ( x − h ) + k ? 2
1
EXPLORATION: Identifying Graphs of Quadratic Functions Work with a partner. Match each quadratic function with its graph. Explain your reasoning. Then use a graphing calculator to verify that your answer is correct. a. g ( x ) = − ( x − 2)
2
2
4
−6
c. g ( x ) = − ( x + 2) − 2
e. g ( x ) = 2( x − 2)
f. g ( x ) = − ( x + 2) + 2
2
d. g ( x ) = 0.5( x − 2) − 2
A.
b. g ( x ) = ( x − 2) + 2
2
2
4
B.
6
−6
−4
−6
4
D. 6
−6
−4
−6
24
Algebra 2 Student Journal
4
F.
6
−4
6
−4
4
E.
6
−4
4
C.
2
−6
6
−4
Copyright © Big Ideas Learning, LLC All rights reserved.
Name_________________________________________________________
2.1
Date __________
Transformations of Quadratic Functions (continued)
Communicate Your Answer 2. How do the constants a, h, and k affect the graph of the quadratic function
g ( x) = a( x − h) + k ? 2
3. Write the equation of the quadratic function whose graph is shown. Explain your
reasoning. Then use a graphing calculator to verify that your equation is correct. 4
−6
6
−4
Copyright © Big Ideas Learning, LLC All rights reserved.
Algebra 2 Student Journal
25
Name _________________________________________________________ Date _________
Notetaking with Vocabulary
2.1
For use after Lesson 2.1
In your own words, write the meaning of each vocabulary term.
quadratic function
parabola
vertex of a parabola
vertex form
Core Concepts Horizontal Translations
Vertical Translations f ( x) = x 2
f ( x) = x 2 f ( x − h) = ( x − h) y = (x − h)2, h0
x2 y = (x − h)2, h>0
y = x 2 + k, k 0
•
shifts up when k > 0
Notes:
26
Algebra 2 Student Journal
Copyright © Big Ideas Learning, LLC All rights reserved.
Name_________________________________________________________
2.1
Date __________
Notetaking with Vocabulary (continued) Reflections in the x-Axis
f ( x) = x
Reflections in the y-Axis
f ( x) = x 2
2
− f ( x) = − ( x 2 ) = − x 2
f ( − x) = ( − x) = x 2 2
y
y = x2
y
x
x
y = – x2
flips over the x-axis Horizontal Stretches and Shrinks
f ( x) = x
y
y = x 2 is its own reflection in the y-axis. Vertical Stretches and Shrinks
f ( x) = x 2
2
f ( ax) = ( ax) y = (ax)2, a>1
y = x2
y=
a • f ( x) = ax 2
2
x2
y = (ax)2, 0
