If a not equal to 0, and y = a (x+h)^2 + c , the graph of

Question

If a not equal to 0, and y = a (x+h)^2 + c , the graph of the equation
intersects the X- axis at how many points?

a. h = 0

b. a < 0

anvar · Answer

cause we don't know anything about c:

a defines direction of parabola branches (up or down), c determines location of a NODE of the curve

Praetorian · Answer

show some mathematical proof

anvar · Answer

Oh, well it is well known that if a<0 branches of parabola go down and if a>0 branches go up. At the same time if c<0, node of parabola is under X axis and if C>0 the Node is above X curve. In other words C defines a shift of parabola along Y curve.

=> even if a<0 it is possible that C<0 also. Therefore, branches of parabola can not cross X axis.

anandnk · Answer

y = a(x+h)^2 + c

for it to intersect with x axis y = 0
so 
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

gmatblast · Answer

Anand,

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.

Thanks

If a not equal to 0, and y = a (x+h)^2 + c , the graph of

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