Question

The vertex of the of the quadratic function f(x)=x^2 is at (0,0), which is a the minimum for the graph of f... to where you predict the vertex will be translate for the graphs of g(x)=(x-2)^2 and h(x)=(x+3)

Answer 1

When there is a number added to or subtracted from x before it is squared, it shifts the graph to the left or right.  For g(x)=(x-2)², the graph would be shifted to the right two units; therefore the vertex would be at (2, 0).  For h(x)=(x+3)², the graph would be shifted to the left three units; therefore the vertex would be at (-3, 0).