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Graph of a Quadratic Equation

f(x) = ax2 + bx + c = 0, where a ≠ 0, and b and c are real coefficients.
 
Description: 8-2.tif
 
As is obvious from the above graphs, when D>0, there are two points at which this curve is intersecting X-axis. And we also know that there are two distinct values of x which satisfy f(x).
 
When D=0, there is only one point at which this curve is intersecting X-axis, and there is only one distinct value of xwhich satisfies f(x).
 
When D<0, there is no point at which this curve is intersecting X-axis. So, there are no real values of x which can satisfy f(x).





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