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

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Answer 1 · 2017-10-15T10:22:30

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

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.