SOLUTION: Find the vertex, the focus, and the directrix of the parabola. 1) y = x2 + 9x + 20

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the vertex, the focus, and the directrix of the parabola. 1) y = x2 + 9x + 20       Log On


   

Question 577699: Find the vertex, the focus, and the directrix of the parabola.
1) y = x2 + 9x + 20

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex, the focus, and the directrix of the parabola.
1) y = x2 + 9x + 20
**
y = x2 + 9x + 20
complete the square
y=(x^2+9x+81/4)+20-81/4
y=(x+9/2)^2+80/4-81/4
y=(x+9/2)^2-1/4
(y+1/4)=(x+9/2)^2
(x+9/2)^2=(y+1/4)
Standard form of equation for a parabola that opens upwards: (x-h)^2=4p(y-k)
vertex:(-9/2,-1/4)
4p=1
p=1/4
directrix: y=-1/2
focus: (9/2,0)