Translation in the direction of the x-axis

Author:
Jing Jie
Move the slider to change the value of A. Observe how the graph changes as the value of A changes.
Activity 1

Observation 1

Describe the change in the graph of y = (x + A)2 when the value of A increases from 0 to 2.

Observation 2

Sketch the graph after this transformation.

Observation 3

Let (0, 0) be a point on the curve y = x2. Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2.

Observation 4

Which value is changed?

Observation 5

What is the replacement of variable involved in transforming the graph of y = x2 to y = (x + 2)2? Replace x by _________
Activity 2

Observation 1

Describe the change in the graph of y = (x + A)2 when the value of A increases from 0 to −3.

Observation 2

Sketch the graph after this transformation.

Observation 3

Let (0, 0) be a point on the curve y = x2. Observe and write down the new coordinates of this point after going through this transformation. Label this point on the transformed graph that you have drawn in Observation 2.

Observation 4

Which value is changed?

Observation 5

What is the replacement of variable involved in transforming the graph of y = x2 to y = (x − 3)2? Replace x by _________
Collect the letters to unlock the solution: The 2nd letter of the password to the solution is U