Vertical and horizontal translations for the parabola
can happen together using both h and k. So, our starting or **
reference** parabola formula looks like this:

**y = x ^{2}**

And our equation that includes both a ** horizontal** and

**y = (x - h) ^{2} + k**

So, if ** h = 3 and k =
4**, we say that the

**y = (x - 3) ^{2} + 4**

Here's the graph for these translations. The ** reference** parabola (

What follows is an animation that presents many horizontal and vertical translations for our reference parabola.

Please understand that ** x^2** means

We see here how the horizontal and vertical
translations of the reference parabola can occur within the same formula.
Here is a calculation for the y-coordinate of the ** transformed** parabola when
the

y = (x - h)^{2} + k

y = (5 - h)^{2} + k

y = (5 - 3)^{2} + (-4)

y = (5 - 3)^{2} - 4

y = 2^{2} - 4

y = 4 - 4

y = 0

Here is an EZ Graph example of these vertical and horizontal translations. Press the 'Draw Graph' button.

You can change the value for ** h** or