What is a quadratic function? (Brief explanation)

A quadratic function is one of the form f (x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

The quadratic function has the form:

F (x) = y = a + bx + cx2

where a, b, and c are numerical constants and c is not equal to zero.

Note that if c were zero, the function would be linear.

An advantage of this notation is that it can easily be generalized by adding more terms. We could for example write equations such as

y = a + bx + cx 2 + dx3

y = a + bx + cx 2 + dx3 + ex 4