Question

What is the difference between `y = -2x^2` and `y = -2x^2 + 4`?

Answer 1

Let's say `f(x)=-2x^2`

So we have `y=f(x)` and `y=f(x)+4`. It is a bit more obvious now that the second function gets moved 4 units up.

In other words `f(x)` is translated by the column vector `[(0),(4)]`

`y=f(x)`:
graph{-2x^2 [-10, 10, -5, 5]}

`y=f(x)+4`:
graph{-2x^2+4 [-10, 10, -5, 5]}