The graph has a y-intercept of 2 and is shifted to the right 6 from the parent function.
The parent function, y=√x, looks like a parabola laid on its side. We generally only consider the positive square root unless told otherwise. Since we have √(x-6) instead of just √x, the graph is shifted to the right 6 units. The +2 at the end of the equation shifts the graph up 2.
Easy
y=a(x-h)^2+k
vertex is (h,k)
we know that vertex is (4,0)
input that point for (h,k)
y=a(x-4)^2+0
y=a(x-4)^2
passes thorugh the point (6,1)
input that point to find a
1=a(6-4)^2
1=a(2)^2
1=a(4)
divide both sides by 4
1/4=a
thefor the equation is
y=(1/4)(x-4)^2
or
y=(1/4)x^2-2x+4
