Question

(x-2)^2 does that equal x^2 - a parabola on a graph?

Answer 1

The graph of (x-2)^2 is just the graph of x^2 shifted to the right by 2 units.

Answer 2

okay and( x +1)(x + 4) would be like (-1) and (-4)?

Answer 3

(-1) and (-4) are roots of ( x +1)(x + 4). That is where the graph will cut the x axis.
Anything of the form ax^2 + bx + c is a parabola. If a is positive, the parabola opens up )U shaped). If a is negative, the parabola open down (inverted U).

If you expand (x+1)(x+4) it will be x^2 + 5x + 4 which is a parabola that opens up and cuts the x axis at x = -1 and x = -4.