y = a(x+h)^2 + c
for it to intersect with x axis y = 0
a(x+h)^2 + c = 0
from condition 1 ) h = 0
so x = sqrt( -c/a ) For this to be real number a < 0 but we dont know either a or c
so 1) is insufficient.
Same holds for 2)
Even if you combine condition 2) just makes x a real number but there infinie possibilities for the values of a and c
SO the answer should be E
I did this problem exactly the same way you did. But I do not understand the last statement in your post (the bold text). I think, even if a < 0, that does not make x a real number. Because it is possible that c < 0. So we cannot answer the question even if after combining the statements. So this does not change the answer. Just wanted to confirm the reasoning.
Please let me know your thoughts.