Question

How do you graph `f(x)=x^2+2`?

Answer 1

`f(x)` has the graph of the standard parabolic function `y=x^2` shifted by 2 units positive ("Up") on the `y-`axis.

Explanation:

`f(x) = x^2+2`

Consider the standard parabolic function `y=x^2` and realise that:

`f(x) =y+2`

Hence, `f(x)` has the graph of the standard parabolic function `y=x^2` shifted by 2 units positive ("Up") on the `y-`axis.

So, `f(x)` is a concave up parabola and has an absolute minimum value of `2` at `x=0`. The graph of `f(x)` is ahown below.

graph{x^2+2 [-13.04, 12.27, -1.41, 11.25]}