At how many points the graph y = ax^2+bx+c intersect x-axis?

[quote="GMATinsight"]At how many points the graph \(y = ax^2+bx+c\) intersect x-axis?

(1) a < 0
(2) c = 6




The question is asking about, how many points the graph intersects X-axis. To make it simpler, we can say, "x" has how many values.

We shouldn't simply say that as the equation is quadratic, "x" has two values, rather you have to calculate the Discriminant of the equation.

For a more detailed explanation of Discriminant Vs Number of solutions:
Here's a quick takeaway with respect to problems given on discriminant and the number of solutions...

For any quadratic equation of the form a\(x^{2}\)+bx+c, the discriminant is \(b^{2}\)-4ac

Let D=\(b^{2}\)-4ac

1) If D>0, then the equation has one solution.
2) If D=0, then the equation has two solutions.
3) If D<0, then the equation has no solution.

Now let's check on the question:

Statement:1

With statement 1, you can't say that D is greater or lesser or equal to 0 unless you know "c" is positive or negative or zero. So, options A and D are out.

Statement:2

Similarly, with statement 2, you can't say that D is greater or lesser or equal to 0 unless you know "c" is positive or negative or zero. So, option B is out.


Now, take both equations combined. Here we know a is negative and c is positive.
W.k.t \(b^{2}\) is always a positive number and "a" being negative, makes the whole discriminant positive. (D=\(b^{2}\)-4ac)

So, we can conclude the answer as Option C.

Hope this helps you.

Good luck!
Vineel

If the graph crosses the Y on 6, and the asymptotes are downward looking (a<0), than the parabola will cross the X axis on two points.

Answer C.

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