In the XY-plane at what 2 points does the graph of y=(x+a)

[Luci]

In the XY-plane at what 2 points does the graph of y=(x+a)(x+b) intersect the x-axis?

(1) (a+b)=1
(2) The graph intersects the Y-axis at (0,-6)

The correct answer is C but I dont understand.

We have y=x^2+x(a+b)+ab this is a parabola of this tipe:





but the origin does not have to be at (0,0) it depends on a and b.

From 1 we get y=x^2+x+ab not sufficient ew dont know what ab is
From 2 if the y intersects are 0 and -6 the raph should be something like this:




and this does not seems to be consistent with the rest of the problem...

Moreover is the y intersects are 0 and -6 the x intersect would be woulb be just 0 as we can see in the second graph...

Gmat prep says that the correct answer is C so I must be missing something

What do you think?

Thanks

[Guest]

y = x^2 + x(a+b) = ab

1. y=x^2 + x + ab NOT SUFFICIENT

2. (0, -6) lies on the graph

-6 = 0+0 + ab
ab = -6 NOT SUFFICIENT

TOGETHER

y = x^2 + x -6

SUFFICIENT

[Luci]

Ok, thanks, I understood it wrong, I thougt that (0,-6) were two points, when it is just one intersect of the Y axis...

That is why the 2 statements were not consistent for me. Now it is clear. Thanks a lot