Question says to find an equation of the parabola:
Vertex (-1, 2); Focus (-1, 0)
How do I do this? I am confused.
Thanks for any help.
You can find the equation by this formula:
$\displaystyle y = a{(x-h)^2}+k $
where, $\displaystyle (h,k)$ is your vertex
and $\displaystyle a= \frac{1}{4d}$ ; d is the distance from the vertex to the focus.
So use distance formula (with the coordinates of your vertex and focus) to find d. You already have (h,k) as your vertex. Plug these values in to get the equation of your parabola.
Try doing it and post a message if you come up with errors
Hi iluvmathbutitshard,
Almost, you missed the sign on "a".
Another way to find "a" in $\displaystyle y=a(x-h)^2+k$
is by knowing that the focus has coordinates $\displaystyle \left(h, k+\frac{1}{4a}\right)$
Set the second coordinate of this ordered pair to the second coordinate of your focus and we have
$\displaystyle 2+\frac{1}{4a}=0$
Solving this, you get $\displaystyle a=-\frac{1}{8}$
Your parabola opens down.
$\displaystyle y=-\frac{1}{8}(x+1)^2+2$