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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.
First, write the equation in standard form, i.e., put zero on the right. Then, depending on the case, you may have the following options:Factor the polynomialComplete the squareUse the quadratic formula
There are many ways: one is to factorise. If the quadratic is written as ax2 + bx + c then, if b2 = 4ac, the quadratic is a perfect square. It is (x - b/2a)2
That depends on what type of equation it is because it could be quadratic, simultaneous, linear, straight line or even differential
Four? Factoring Graphing Quadratic Equation Completing the Square There may be more, but there's at least four.