Answer:
(1,4)
Step-by-step explanation:
Let's this of [tex]y=\sqrt{x}[/tex] which is it's parent function.
How do we get to [tex]y=-\sqrt{x-1}+4[/tex] from there?
It has been reflected about the a-axis because of the - in front of the square root.
It has been shifted right 1 unit because of the -(1) in the square root.
It has been moved up 4 units because of the +4 outside the square root.
In general:
[tex]y=a(x-h)^2+k[/tex] has the following transformations from the parent:
Moved right h units if h is positive.
Moved left h units if h is negative.
Moved up k units if k is positive.
Moved down k units if k is negative.
If [tex]a[/tex] is positive, it has not been reflected.
If [tex]a[/tex] is negative, it has been reflected about the x-axis.
[tex]a[/tex] also tells us about the stretching factor.
The parent function has a starting point at (0,0). Where does this point move on the new graph?
It new graphed was the parent function but reflected over x-axis and shifted right 1 unit and moved up 4 units.
So the new starting point is (0+1,0+4)=(1,4).
