Sketch the graph of each function.

Question

Y=(x-3)^2-1

Answer 1

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=x^2, 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:

 

http://www.wyzant.com/resources/files/291690/graph_of_parabola