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

Algebra ->  Functions -> 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      Log On


   

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 %28x+-+h%29%5E2 = 4p(y - k).]

Answer by josgarithmetic(39617) About Me  (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 y=a%28x-%28-1%29%29%28x-3%29
y=a%28x%2B1%29%28x-3%29
and then
a%28x%2B1%29%28x-3%29=y
a%280%2B1%29%280-3%29=-12
a%2A1%2A%28-3%29=-12
a=-12%2F%28-3%29
a=4
For the equation highlight_green%28y=4%28x%2B1%29%28x-3%29%29. This is in FACTORED form, but you next want to adjust into Standard Form, using simplification and then Completing The Square.

y=4%28x%5E2-2x-3%29
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.
-
y=4%28x%5E2-2x%2B1-1-3%29
y=4%28%28x-1%29%5E2-4%29
y=4%28x-1%29%5E2-16-----Standard Form
and then
highlight%28y%2B16=4%28x-1%29%5E2%29

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 highlight%28%28x-1%29%5E2=%281%2F4%29%28y%2B16%29%29 and in this way, your 4p will be equal to 1%2F4, and you can find the value and meaning for p.