Investigate the Graphs of Quadratic Functions

In this activity you will investigate the graphs of quadratic functions in the form

f(x) = a(x - h)

2

+ k

You will be assessing the changes in both the

shape

and

position

of the graph.

Procedures

Go to the

Desmos

online graphing calculator. Link:

https://www.desmos.com/calculator/

In the first space on the left type in the equation above.

Click on "all sliders" to enable them. You can now adjust the values of a, h, and k

manually.

First focus on

a

.

Set both

h

and

k

to zero. Change the value of

a

(make it both positive and negative).

1. On your paper describe in complete sentences how

a

affects the

shape

and

position

of

the graph. Please describe all the noticeable effects as clearly as you can.

Now focus on

k

.

Set

a

= 1 and

h

= 0. Change the value of

k

(make it both positive and negative).

2. On your paper describe in complete sentences how

k

affects the

shape

and

position

of

the graph. Please describe all the noticeable effects as clearly as you can.

Focus on

h

.

Set both

a

=1 and

k

= 0. Change the value of

h

(make it both positive and negative).

3. On your paper describe in complete sentences how

h

affects the

shape

and

position

of

the graph. Please describe all the noticeable effects as clearly as you can.

Analysis: Answer the following questions on your paper.

4. Which of the variables

a, h

and

k

change the position of the graph (translate the graph)?

5. Which of the variables

a, h

and

k

change the shape of the graph by stretching?

Additional Questions: Answer the following questions on your paper.

6. What did you find out? (What do you know now that you didn't before this activity)

7. What seems correct?

8. What seems wrong?

9. What do you still need to find out? What are you unsure of?