Hi Sri,

First off, this type of graphing isn't too common on the Official GMAT, so you shouldn't worry about seeing it on Test Day.

This DS question is based on some graphing properties though:

The equation y = a(x^2) + bx + c is NOT a straight line.

The a(x^2) part of the equation tells us that the shape will be symmetrical around some vertical line. If "a" is positive, then the graph will "open upwards"; if "a" is negative, then the graph will "open downwards."

The c part of the equation gives us the Y-intercept, which means the graph could "start" above the x-axis (if c is positive), on the x-axis (if c is 0) or below the x-axis (if c is negative).

Until we have specifics about those pieces of information, we'll have no way to know how many times the graph intersects the x-axis.

Fact 1: A > 0

This tells us that the graph "opens upwards", but we don't know the Y-intercept.

It's possible that the graph has 0 points that intersect the x-axis (if c > 0).
It's possible that the graph has 1 point that intersects the x-axis (if c = 0).
It's possible that the graph has 2 points that intersect the x-axis (if c < 0).
Fact 1 is INSUFFICIENT

Fact 2: C < 0

This tells us that the graph "starts" below the x-axis, but we don't know if it opens "upwards" or "downwards"

It's possible that the graph has 0 points that intersect the x-axis (if a < 0).
It's possible that the graph has 2 points that intersect the x-axis (if a > 1).
Fact 2 is INSUFFICIENT

Combined, we know that A > 0, so the graph opens "upwards" and C < 0, so the graph begins below the x-axis.
We now know that the graph intersects at 2 points on the x-axis.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich