How do you sketch the graph of y=(x-2)^2+3 and describe the transformation?

1 Answer
Oct 15, 2017

Shift to the right by 2 units, vertical translation upwards by 3 units.

Explanation:

The parent function of the graph is y=x^2.

Using the general equation y=af(k[x-d])+c,

Where if a > 1=vertical stretch,
0< a < 1= vertical compression.

-f(x)=reflection in the x-axis
f(-x)=reflection in the y-axis.

0 < k < 1= horizontal stretch,
k > 1= horizontal compression.

-d=horizontal shift to the right
d= horizontal shift to the left

c= vertical translation upwards
-c=vertical translation downwards.

Using this, we can see that the graph has a horizontal shift 2 units to the right and a vertical translation of 3 units upwards.