Which of the following parabolas opens up?

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

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

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

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

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.

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