Shifting the Input

Here is $f\left(x\right) = {x}^{2}$. Its lowest point is (0, 0). Now put $x-3$ into f instead of x. This gives $y = f\left(x-3\right)$. Does the curve move left or right? Most people say left, because of the minus sign.

You can work it out. The curve of f is lowest when the input of f is 0. So find the x that makes $x-3$ equal to 0. At that x the curve has its lowest point, called the vertex. The curve keeps the same shape.