simplify y=√(4x-x^2)

Question

Hi I need help simplifying this equation 

Answer 1

y=√(4x-x²)

 

I don't think you want to simplify it, I think you want to put it into the standard form for a circle:

 

     (x-h)² + (y-k)² = r²

 

Square both sides:

 

     y² = 4x - x²

     x² - 4x + y² = 0

 

Now complete the square for the x terms.  The square for y term (y²) is already completed:

 

    x² - 4x + (-2)² + y² = 0 + (-2)²

    x² - 4x + 4 + y² = 4

 

    (x-2)² + y² = 4

 

This is the equation of circle with center at (h,k) = (2,0) and radius = √4 = 2.

Answer 2

Hi, Sam. In order to simplify, you must factor out x from 4x - x^2. Try it and see what your new equation looks like.