Chelsea is trying to find the equation of a quadratic that has a focus of (1, 3) and a directrix of y = –3. Describe to Chelsea your preferred method for deriving the equation. Make sure you use Chelsea's situation as a model to help her understand

Question

anonymous · Answer

you need to know what this looks like first
plot the focus and directrix to see which way the parabola opens, then it is easy to find the equation
lets draw the picture

anonymous · Answer

|dw:1416628357689:dw|

anonymous · Answer

now we know it faces up
the $x$ term is squared, and the vertex is halfway between $(1,3)$ and $y=-3$ namely at $(1,0)$

anonymous · Answer

the equation is therefore 
$$4py=(x-1)^2$$ and all you need is $p$ which is the distance from the focus to the directrix, namely 3 so final answer is 
$$12y=(x-1)^2$$ lets check it

anonymous · Answer

yup it is right http://www.wolframalpha.com/input/?i=parabola+12y%3D%28x-1%29^2