Is there a parent function for this equation -

Question

y = 2+sqrt(25-(x+3)^2)

Answer 1

Assuming the function you have given is a result of several transformations, there is a parent function.  The parent function is the reference function that you use to make the transformation.  Notice the square-root part in the transformed function.  This tells us that we started with a function that acts as a square-root function.  So the parent function must be

 

y = √(x)

 

From this function, you would perform vertical shifts, horizontal shifts, and stretches to get the desired transformation.

 

 

EDIT:

 

After reviewing the function in detail, I noticed that this function can be rearranged so that it becomes a circle.

 

Subtract 2 on both sides of the equation.

 

y - 2 = √(25 - (x + 3)²)

 

 

Square both sides of the equation to undo the square-root.

 

(y - 2)² = 25 - (x + 3)²

 

 

Add (x - 3)² on both sides of the equation.

 

(x + 3)² + (y - 2)² = 25

 

 

Now you have a circle with a radius of 5 and centerpoint at (-3, 2).

 

 

The function you have given represents the upper half of the circle.