Question

Which of the following parabolas opens up?

Answer 1

B. Directrix: y=2; focus (3,5)

Answer 2

The focus-directrix form of a quadratic equation is
(x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p

the parabola opens upward when p is a positive number.
plug the numbers in k+p and k-p, you will see only B produces a positive p value:
for B: k+p=5, k-p=2
solve for p by subtract the second equation from the first equation:
2p=3, p=1.5, a positive number
the others will all produce a negative p value, so B is the only answer.