SOLUTION: I'm trying to sketch a graph of a semicircle and determine its center points and radius. The equation is y=square root of (-12x-x^2). My book doesn't explain semicircles. Please he

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I'm trying to sketch a graph of a semicircle and determine its center points and radius. The equation is y=square root of (-12x-x^2). My book doesn't explain semicircles. Please he      Log On


   

Question 943060: I'm trying to sketch a graph of a semicircle and determine its center points and radius. The equation is y=square root of (-12x-x^2). My book doesn't explain semicircles. Please help! Thanks!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first, write it in the form %28x-h%29%5E2+%2B%28y-k%29%5E2=r%5E2 then (h,k) is the center and r is the radius
y=sqrt+%28-12x-x%5E2%29 ..... square both sides

y%5E2=-12x-x%5E2
x%5E2%2B12x%2By%5E2=0
%28x%5E2%2B12x%2B_%29-_%2By%5E2=0+ complete square
%28x%5E2%2B12x%2B6%5E2%29-36%2By%5E2=0
%28x%2B6%29%5E2%2By%5E2=36
%28x%2B6%29%5E2%2B%28y-0%29%5E2=6%5E2
center (-6,0) and radius of r=6

To sketch, plot the center. The radius is r=6 so go out 6 units in each direction until you have enough points to draw in the graph, or use a compass.
few more points
(-12,0)
(-6,6)
(0,6)