Philip P. answered 09/25/14
Affordable, Experienced, and Patient Algebra Tutor
y = (x-3)2 - 1
y+1 = (x-3)2
This is the equation of a parabola in vertex form: y-k = a(x-h)2 where (h,k) is the location of the vertex. In this case a=1 which means the parabola opens upward (downward if a<0) and has the same shape as y=x2, but the vertex is shifted to the point (3,-1).
You could also evaluate this as a function transformation. f(x-3) shifts f(x) 3 units to the right on the x-axis. f(x) - 1 shifts f(x) down one on the y-axis. Click on the link below to see the graph: