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

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 $y = a f \left(k \left[x - d\right]\right) + c$,

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

$- f \left(x\right) =$reflection in the $x$-axis
$f \left(- x\right) =$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.