What is the definition of standard form in math?

There are many standard forms in mathematics. A common standard form is the standard form equation of a line, following the pattern of Ax + By = C, where A and B are not zero.

The standard form of a linear equation, Ax + By = C, has useful features. It gives an easy way to derive the X and Y intercepts because one can plug in zero for either X or Y to calculate the value of the other variable. This makes it easy to graph the line. The standard form of a quadratic is in the form Ax^2 + Bx + C = 0. This is a useful form because the X value of the vertex of a quadratic is -b/(2a) and the X values of the equations' intersections with the x-axis are (-b +/- sqrt(b^2 - 4ac) ) / (2a).