Question

How to graph a parabola `y = (x - 2)^2 + 1`?

Answer 1

See below

Explanation:

First, graph the parent function `y=x^2`

graph{x^2 [-10, 10, -5, 5]}

Then, we transform the graph based on the problem. The `-2` on the inside signifies a shift to the right by `2`. The 1 on the outside signifies a shift upward by 1. So our graph becomes more like:

graph{((x-2)^2)+1 [-10, 10, -1, 9]}