SOLUTION: Currently, we are working on horizontal parabolas. I am supposed to find the vertex, focus, and directrix of this formula: {{{ y^2-y-x+6=0 }}} I've been working the equation, an

Question 854090: Currently, we are working on horizontal parabolas. I am supposed to find the vertex, focus, and directrix of this formula:
I've been working the equation, and my work currently looks like this:

I don't know what to do with the 23/4. Any help would be appreciated :) Thank you!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the vertex, focus, and directrix of this formula:
y^2-y-x+6=0
complete the square:
(y^2-y+(1/4))-x+6=0+1/4
(y-(1/2)^2=x+(1/4)-6

This is an equation of a parabola that opens right.
Its basic form of equation: , (h,k)=coordinates of the vertex
For given problem:
vertex:((23/4),(1/2))
axis of symmetry: y=(1/2)
4p=1
p=1/4
focus: ((24/4),(1/2))=(6,(1/2)) (p-distance to the right of vertex on the axis of symmetry)
directrix: x=(22/4)=11/2 (p-distance to the left of vertex on the axis of symmetry)
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