SOLUTION: Please help me use completing the sq. to write the equation in the form y=a(x-h)^2+k. Also identify the vertex, focus and directrix. y=3x^2=12x=1.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please help me use completing the sq. to write the equation in the form y=a(x-h)^2+k. Also identify the vertex, focus and directrix. y=3x^2=12x=1.       Log On


   

Question 64380: Please help me use completing the sq. to write the equation in the form y=a(x-h)^2+k. Also identify the vertex, focus and directrix.
y=3x^2=12x=1.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me use completing the sq. to write the equation in the form y=a(x-h)^2+k. Also identify the vertex, focus and directrix.
y=3x^2=12x=1.
Comment: You probably posted this with a mistake. I'm going to
assume you meant y=3x^2+12x+1
Rewrite as:
3x^2+12x=y-1
3(x^2+4x = y-1
x^2+4x+? = (1/3)(y-1)+?
Complete the square to get:
x^2+4x+4=(1/3)(y-1)+4
(x+2)^2=(1/3)(y-1+12)
(x+2)^2=(1/3)(y+11)
Vertex: (-2,-11)
4p=1/3
p=1/12
Focus: (-2+1/12,-11) = (-23/12,-11)
Directrix: y=-11-1/12 = -(11 1/12)
graph%28300%2C200%2C-10%2C10%2C-20%2C20%2C3x%5E2%2B12x%2B1%29
Cheers,
Stan H.