Question 774071: What is exactly is a quadratic equation? What is the standard form of a quadratic equation? Why is tit important to be able to write a quadratic equation in standard form?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! A quadratic equation is a second order polynomial, actually a trinomial. It is second order because the largest exponent of the variable in the polynomial is two as in  . The standard form is
(1)  , where a, b and c are real valued numbers.
The prefix "quad" is usually associated with the number four as in a four sided quadrangle. However in this case "quad" is based on the prefix taken from the Greek variation for two or square.
The reason for the standard form is to put all mathematics users, eg engineers and physicists on the same page. Most computer programs are designed to solve the quadratic equation using the "quadratic equation", defined by the use of a, b and c as the coefficients as given in (1).
(2)
The quadratic equation always (if "a", the coefficient of is not equal to zero) factors into two factors, albeit the constants in the factors may not be real, but (thankfully) can be complex.
The straight line (a binomial) and the quadratic (a trinomial) are the most useful of all polynomials because all higher order polynomials can be factored into these two basic forms.
This is why we spend so much time/study on the straight line and a fair amount of time on the non-complex form of the quadratic called a "parabola". Later in Algebra II, you will learn about compex numbers, etc.
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