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1 vote
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)

2 Answers

1 vote
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.


User Parth Bhatt
by
6.1k points
6 votes
B. Directrix: y=2; focus (3,5)
User Kanishk
by
6.0k points
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