Question

What is the range of the graph of y = (x - 4)^2 + 3

Answer 1

Well its a quadratic first of all.

Answer 2

That should give you a hint on how the graph should look like

Answer 3

think about it conceptually. "(x - 4)^2" is strictly positive and will increase as the absolute value of x goes further from 4. Even if "(x - 4)^2" =0 when x=4, y=3.

Therefore, there won't be an instance where y<3 yet "(x - 4)^2" keeps growing without bound.