Answer:
y = -3√(x -1) +2
Explanation:
You want the equation of the given square root function with its vertex at (1, 2) and point (2, -1) on the graph.
Square root function
The parent square root function has its vertex at (0, 0). It extends upward from that vertex, and goes through the point (1, 1).
Transformed function
The function shown in the graph has its vertex at (1, 2), so has been translated 1 unit to the right and 2 units upward. The function extends downward from the vertex, so has been reflected vertically.
We know a function translated h units right and k units up becomes ...
g(x) = f(x -h) +k
When it is reflected across the x-axis, it also has a multiplier (-a):
g(x) = -a·f(x -h) +k
Scale factor
We can find the value of 'a' by using the given point in the translated function.
g(x) = -a·√(x -1) +2
-1 = -a√(2 -1) +2
-3 = -a√1 = -a
The value of 'a' is 3.
The graph is described by the function ...
y = -3√(x -1) +2