SOLUTION: the vertex of the parabola x2+6x+3y+r=0 is on the x-axis. Find r.

Algebra ->  Equations -> SOLUTION: the vertex of the parabola x2+6x+3y+r=0 is on the x-axis. Find r.       Log On


   

Question 1017075: the vertex of the parabola x2+6x+3y+r=0 is on the x-axis. Find r.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Vertex of a parabola on the x-axis means ONE root only, REAL, and therefore
the discriminant is 0.

x%5E2%2B6x%2B3y%2Br=0
3y=-x%5E2-6x-r
y=-%281%2F3%29x%5E2-2x-%281%2F3%29r

Discriminant here is
%28-2%29%5E2-4%2A%28-1%2F3%29%28-1%2F3%29r
4-4r%2F9

You want to equate this expression, the discriminant, to 0.
4-4r%2F9=0
4=4r%2F9
1=r%2F9
highlight%28r=9%29