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2.1 Graphing Calculator Activity

Linear Parent Graph Transformations

y = x is called the linear parent function.

x y

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0

1

1. Clear the y= menu and then graph y = x.

2. Graph y = x + 2 and describe the change to y = x. _________________________________________

Graph y = x - 3 and describe the change to y = x. _________________________________________

Note: When a graph is "slide" right/left or up/down, we call this movement a translation.

3. Write a linear function which is a translation down 5 units of the parent function. y = __________

Write a linear function which is a translation up 7 units of the parent function. y = ____________

4. Multiple Choice: y = x + k where k is a constant describes a _____.

A. vertical translation: the graph is "slid" up or down;

B. horizontal translation: the graph is "slid" right or left;

C. reflection: the graph is "flipped" over some line;

D. rotation: the graph is "spun" like the hands of a clock.

Quadratic Parent Graph Transformations

y = x2 is called the quadratic parent function.

x y

-2

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1. Clear the y= menu and then graph y = x2. This is a U-shaped curve called a ____________________.

2. Graph y = x2 + 2 and describe the change to y = x2. _______________________________________

Graph y = x2 - 3 and describe the change to y = x2. _______________________________________

3. Write a quadratic function which is a translation down 5 units of the parent function.

y = __________________

Write a quadratic function which is a translation up 6 units of the parent function.

y = __________________

4. Multiple Choice: y = x2 + k describes a _____.

A. vertical (up/down) translation C. reflection

B. horizontal (left/right) translation D. rotation

5. Clear the y= menu then graph y = x2.

6. Graph y = (x - 2)2 and describe the change to y = x2. _____________________________________

Graph y = (x + 3)2 and describe the change to y = x2. _____________________________________

7. Write a quadratic function which is a translation right 5 units of the parent function.

y = ____________________

Write a quadratic function which is a translation left 6 units of the parent function.

y = ____________________

8. Multiple Choice: y = (x - k)2 describes a _____.

A. vertical (up/down) translation C. reflection

B. horizontal (left/right) translation D. rotation

9. Open the book to page 60 and read the box at the top of the page concerning translations.

Complete the graphic organizer.

Translations of Quadratic Functions

Horizontal Translations Vertical Translations

Horizontal Shift of |_____| units Vertical Shift of |_____|units

f(x) = x2

f(x) = x2

f(x) + ___ = x2 + ___

f(x - ___) = (x - ___)2

Moves down for

Moves left for ___ < 0

___ < 0 Moves up for

Moves right for ___ > 0

___ > 0

10. Open the book to page 60 and read example 2.

Using what you have learned and the graph of y = x2 as a guide, describe the transformations in

each of the following. Then graph each function using the graphs provided.

a. g(x) = (x - 2)2 + 4 ________________________________________________________

b. g(x) = (x + 2)2 - 3 ________________________________________________________

Steps to graph:

1. Plot the ordered pairs of the parent function y = x2.

2. Shift each ordered pair of the parent function according to the transformations described.

3. Sketch the curve containing the transformed ordered pairs.

Recall: y = x2 is the quadratic parent function.

Recall: y = (x - h)2 + k describes a translation horizontally h units and vertically k units.

11. Clear the y= menu and then graph y = x2.

12. Graph y = -x2 and describe the change to y = x2. ___________________________________

Notes: When a graph is "flipped" over a line, we call this movement a reflection and the line in which

the graph is reflected is called the line of reflection.

13. What is the equation of the line of reflection for y = -x2. ____________________________

Hint: vertical lines have equation x = some number and horizontal lines have equation y = some number.

14. Multiple Choice: y = -(x - h)2 + k would be a _____ of y = (x - h)2 + k.

A. vertical (up/down) translation C. reflection over the x-axis

B. horizontal (left/right) translation D. reflection over the y-axis

15. Graph y = (-x)2 and describe the change to y = x2. __________________________________

Notes: Based on the previous work, the negative sign should indicate a reflection.

Notes: There appeared to be no flip because y = x2 is symmetric about the y-axis. If we use a function

which is not symmetric about the y-axis this "flip" should be visible.

Author: Patricia Harmon

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