Answer:
-f(x +6) +2
Explanation:
You want the expression that transforms the function y = √x so that its vertex is (-6, 2) and it is reflected vertically.
Translation
A function's graph is translated (right, up) by (h, k) this way:
f(x -h) +k
The desired function has been translated left 6 units and up 2 units, so we have (h, k) = (-6, 2).
Vertical reflection
A function's graph is reflected vertically (made upside down) by multiplying each function value by a negative number. Here, there is only reflection, without any vertical scaling, so the multiplier is simply -1.
Red curve
The reflected and translated graph will be created by the transformation ...
-f(x +6) +2
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Additional comment
Effectively, we have translated the reflected graph. If we wanted to reflect the translated graph, we would apply the minus sign to the translated function:
-(f(x +6) +2)