Quadratic functions

Let us first see how quadratic functions are defined. A function is a relation between two or more variables which is one to one and onto. If the independent variable is single with degree 2 and the dependent variable is of degree 1, then the function is said to be quadratic. That is, the output of the function is related to the square of the input.

The general form of a quadratic function is y = f(x) = ax2 + bx + c, where a, b and c are all constants. Obviously, the constant a cannot be 0, in which case the degree of the variable will be no longer 2 and hence the function will not qualify as quadratic function.

Quadratic-functions are the most prominent functions in algebra as many practical situations can be cited as quadratic functions examples. Thus the knowledge of solving quadratic functions is extremely important. The solving can mean in two types of solving. One is to find y for a given value of x. But this is very simple task to do and has no great practical implications.

On the other hand, for a given value of y, to solve forx is extremely important. This is what generally referred as solving quadratic functions. The very first exercise is to solve for solve for x,when y = 0. The values of x under such conditions are called as the zeroes of the function or the x-intercepts of the function. In case of linear functions y-intercepts are more prominent but in case of functions of quadratic form, the x-intercepts are more prominent.

In certain cases, you may find the solutions to be imaginary and at a later stage we will explain the implication of such cases.

A quadratic function can be transformed to a quadratic equation for a given value of y. That is, the constant term is adjusted accordingly and is equated to 0. There are many methods of solving for the variable. The easiest method, if possible, is to factor the trinomial as the product to two binomials and apply the zero product property. In cases where factorization is not possible, one can use the quadratic formula and find the solutions.

We cannot predict for sure, the shape of a graph for a given function except in two cases. In case of a linear function, the graph is a straight line. The shapes of graphs of quadratic functions are invariably vertical parabolas. The points of intersections of the parabolas with x-axis are the zeroes of the function. If there are no such intercepts, the zeroes of the functions are imaginary.