general rule for translating a parabola left and right

Question

what is the general rule for translating a parabola left and right?

Answer 1

A rule for any function (not just a parabola):

 

Let a > 0.

 

f(x - a) has the same profile as f(x), but shifted a units in the +x direction.  

 

f(x + a) has the same profile as f(x), but shifted a units in the -x direction.

 

If you have trouble visualizing this, pick a simple function f(x), plot it, and then plot something like f(x - 1) and f(x + 1), and compare the profiles.

Answer 2

This is from the Internet:

 

y = x^2

And our equation that includes a horizontal translation looks like this:

y = (x - h)^2

So, if h = 6, we say that the reference parabola is horizontally translated by 6 units, and our equation for this would appear:

y = (x - 6)^2