What are the different forms in quadratic equation?

Answer 1

The general form of a quadratic equation is y = ax2 + bx + c, where a, b and c are real constants and a ≠ 0. If a = 0 then it is not a quadratic!

There are two ways of classifying the forms.

"CUP OR CAP"

If a > 0 then the graph of the quadratic is cup shaped - like a U.

If a < 0 then the graph is cap shaped - like an inverted U.

"NUMBER OF ROOTS"

Using the above form, calculate the discriminant, d = b2 - 4ac

If d > 0 the quadratic has two real roots. That is, two distinct real values of x for which y = 0.

If d = 0 the quadratic has two coincident real roots. (Some consider this as one root but it is useful to consider the situation as two roots that coincide since that approach maintains parity between the number of roots and the order of the polynomial.)

If d < 0 there are no real roots. Instead, it has two complex roots which will be conjugates of one another.