SOLUTION: Please help me with this problem also: Find the coordinates of the focus and the equation of the directrix of the parabola which crosses the x axis at x = -1 and x = 3 and which c

Question 993650: Please help me with this problem also:
Find the coordinates of the focus and the equation of the directrix of the parabola which crosses the x axis at x = -1 and x = 3 and which crosses the y axis at y = -12.[ Hint: first find the equation of the parabola and then write it in the form = 4p(y - k).]

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You can adjust the form after you find the equation using your given data.

You have an unknown factor, "a" which fits

and then

For the equation . This is in FACTORED form, but you next want to adjust into Standard Form, using simplification and then Completing The Square.

and the term to add and subtract inside the parentheses will be 1.
Why, see this Lesson includes how to complete the square to put into standard form.
-

-----Standard Form
and then

Now you want to determine the focus and directrix. I suggest you check these two video presentations which explain this more:
-
parabola, directrix and focus, with the vertex at origin
-
parabola equation using focus and directrix but now vertex not at origin

Understand that your equation put into the appropriate form will be and in this way, your will be equal to , and you can find the value and meaning for p.
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