SOLUTION: Determined the vertex,focus,directrix,and axis’s of semmetry of the parabola with given equation .sketch the graph and include these points and lines (y+5/2)^2=-5(x-9/2)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Determined the vertex,focus,directrix,and axis’s of semmetry of the parabola with given equation .sketch the graph and include these points and lines (y+5/2)^2=-5(x-9/2)      Log On


   

Question 1169284: Determined the vertex,focus,directrix,and axis’s of semmetry of the parabola with given equation .sketch the graph and include these points and lines

(y+5/2)^2=-5(x-9/2)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28y%2B5%2F2%29%5E2=-5%28x-9%2F2%29 .......compare to 4p%28x-h%29=%28y-k%29%5E2 , you see that h=9%2F2+and+k=-5%2F2
the vertex is at (9%2F2 , +-5%2F2)
and
4p=-5
p=-5%2F4

The focus of parabolas in this form have a focus located at
( h+%2B+p , k ) =>
(+9%2F2+-5%2F4 , -5%2F2 ) =( 18%2F4+-5%2F4 , -5%2F2 ) =(+13%2F4+, -5%2F2+)
and a directrix at x+=+h+-+p+
x+=+9%2F2+-+%28-5%2F4%29++
x+=+9%2F2+%2B5%2F4+
x+=+18%2F4+%2B5%2F4+
x+=23%2F4

The axis of symmetry is located at y+=+k .

since k=-5%2F2
y+=+-5%2F2