SOLUTION: how do you find the vertex, focus and directrix of a parabola in the form {{{ x^2 + 6x - 4y + 1 = 0 }}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: how do you find the vertex, focus and directrix of a parabola in the form {{{ x^2 + 6x - 4y + 1 = 0 }}}      Log On


   

Question 832102: how do you find the vertex, focus and directrix of a parabola in the form
+x%5E2+%2B+6x+-+4y+%2B+1+=+0+
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+6x+-+4y+%2B+1+=+0
4y=x%5E2%2B6x%2B1
Complete the square in x,
4y=%28x%5E2%2B6x%2B9%29%2B1-9
4y=%28x%2B3%29%5E2-8
y=%281%2F4%29%28x%2B3%29%5E2-2
The vertex is therefore at (-3,-2)
4y%2B8=%28x%2B3%29%5E2
4%28y%2B2%29=%28x%2B3%29%5E2
The distance from the vertex to the focus is 4.
Since the parabola opens up, the focus is (1,-2).
The directrix is then y=-7