SOLUTION: Identify the curve and find the center, directix, and focus. Then sketch the curve. {{{(y-2)^2=(x-3)}}} Thank you!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Identify the curve and find the center, directix, and focus. Then sketch the curve. {{{(y-2)^2=(x-3)}}} Thank you!      Log On


   

Question 803351: Identify the curve and find the center, directix, and focus. Then sketch the curve.
%28y-2%29%5E2=%28x-3%29
Thank you!
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
A parabola comparable to y%5E2=x, but the vertex is at (3,2).

A standard derivation would typically be y%5E2=4px in which p is the distance from vertex to directrix and from vertex to focus point. In your example, 4p=1, so p=1%2F4.

To finish, center is (3,2), focus is at (3.25,2) and directrix at x=2.75. The parabola opens toward the right.


Graphing relies on finding two functions:
y-2=0%2B-+sqrt%28x-3%29
y=2%2B-+sqrt%28x-3%29
highlight%28y=2-sqrt%28x-3%29%29 and combine with highlight%28y=2%2Bsqrt%28x-3%29%29.

graph%28400%2C400%2C-12%2C12%2C-12%2C12%2C2-sqrt%28x-3%29%2C2%2Bsqrt%28x-3%29%29