Question 993650
You can adjust the form after you find the equation using your given data.


You have an unknown factor, "a" which fits  {{{y=a(x-(-1))(x-3)}}}
{{{y=a(x+1)(x-3)}}}
and then
{{{a(x+1)(x-3)=y}}}
{{{a(0+1)(0-3)=-12}}}
{{{a*1*(-3)=-12}}}
{{{a=-12/(-3)}}}
{{{a=4}}}
For the equation {{{highlight_green(y=4(x+1)(x-3))}}}.   This is in FACTORED form, but you next want to adjust into Standard Form, using simplification and then Completing The Square.


{{{y=4(x^2-2x-3)}}}
and the term to add and subtract inside the parentheses will be 1.
Why, see this <a href="http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev">Lesson includes how to complete the square to put into standard form</a>.
-
{{{y=4(x^2-2x+1-1-3)}}}
{{{y=4((x-1)^2-4)}}}
{{{y=4(x-1)^2-16}}}-----Standard Form
and then
{{{highlight(y+16=4(x-1)^2)}}}


Now you want to determine the focus and directrix.  I suggest you check these two video presentations which explain this more:
-
<a href="https://www.youtube.com/watch?v=M8LGsQMwwj4">parabola, directrix and focus, with the vertex at origin</a>
-
<a href="https://www.youtube.com/watch?v=Wworlx39KfQ">parabola equation using focus and directrix but now vertex not at origin</a>


Understand that your equation put into the appropriate form will be {{{highlight((x-1)^2=(1/4)(y+16))}}} and in this way, your {{{4p}}} will be equal to  {{{1/4}}}, and you can find the value and meaning for p.