SOLUTION: i need help with step by step. the teacher didnt do it step by step he did problems in his head and just put the answers on the board and i have been stuck on homework. find verte

Click here to see ALL problems on Quadratic-relations-and-conic-sections

Question 538472: i need help with step by step. the teacher didnt do it step by step he did problems in his head and just put the answers on the board and i have been stuck on homework.
find vertex, focus, and directrix of each parabola
(y-3)^2 = 12x
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
i need help with step by step. the teacher didnt do it step by step he did problems in his head and just put the answers on the board and i have been stuck on homework.
find vertex, focus, and directrix of each parabola
(y-3)^2 = 12x
**
Standard form of an equation for a parabola: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex. Parabola opens rightwards with axis of symmetry horizontal.
For given equation:
vertex: (0,3)
axis of symmetry: y=3
4p=12
p=3
Focus:(3,3) (p units from vertex on the axis of symmetry)
Directrix: x=-3 (A vertical line p units from the vertex on the axis of symmetry)
see graph below as a visual check on the answers:
y=�(12x)^.5+3