In an xy-plane, how many points are common to the x-axis and the curve

How many points are “common to the X axis and the curve” essentially means how many times will the parabola cross and intersect the X Axis


By finding the points for X Values that make Y = 0, we will find the X Intercepts.


Setting the Quadratic equal to 0 and solving for the Solutions for X will let us know how many times the parabola intersects the X-Axis.

By using the Discriminant (the value under the square root sign in the quadratic formula) we can see how many times the parabola will cross the X Axis

If: (b)^2 - 4ac = 0 ———- will cross X Axis 1 Time


If: (b)^2 - 4ac > 0 ———— will cross X Axis 2 Times

If: (b)^2 - 4ac < 0 ————- the parabola will never cross the X Axis


S1: just knowing that b is negative does not tell us which of the 3 cases we have. It can be any of the above.

NOT Sufficient.

S2: c < 0

Given that the coefficient for A in front of (x)^2 is equal to 1, we have:

(b)^2 - 4 (1) (- negative value)

The result of the Discriminant will always be Positive and we know that the Parabola will cross the X Axis 2 Times

B s2 alone sufficient

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