Question

How do you sketch the graph of `y=(x-1)^2` and describe the transformation?

Answer 1

Graph the equation of `x^2`, then shift it to the right by 1.

Explanation:

`a(x-h)^2 + b`

Remember this formula? It comes with many variations, but the basic idea is the same. `a` is the vertical stretch of the function; `h` is the horizontal shift, and `b` is the vertical shift.

In the equation `(x-1)^2`, we have only one thing to worry about, which is the horizontal shift `h`. Since `h` is negative, (`-1`), it is actually a positive shift, to the right. Since there are no other shifts, all you have to do is graph the equation of `x^2`, then shift it to the right by 1!