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Standard (General) form of a quadratic expression

Introduction
When the terms in a quadratic expression are written in descending order of their
respective exponents, the resulting quadratic expression is said to be in its standard
form or in its general form. The standard form (general form) of a quadratic expression
is a s follows:
ax2 + b + c
In the above expression, 'a', 'b' and 'c' are numbers and 'a' should not be equal
to 0, otherwise the expression will not remain quadratic (since the highest exponent
will not be equal to zero as 0x2 = 0)


Examples
  • For example, in the following expression, a = 2, b = 3 and c = 1:
    2x2 + 3x + 1
  • In the following quadratic expression, a = -2, b = -3 and c = -1:
    -2x2 - 3x - 1
  • In the following expression, a = 1, b = 1 and c = 1:
    x2 + x + 1
  • In the following expression, a = 1/2, b = 1/3 and c = 1/6:
    x^2/2 + x/3 + 1/6
Converting a quadratic expression to its standard form
In order to convert any quadratic expression to its standard form, you need to follow the following general steps:
  • Remove any parenthesis by applying distribution or FOIL, as appropriate
  • Rewrite the expression in descending order of exponents
Let us discuss an example to understand the above procedure:

Example:
Given quadratic: 4 + x(3 + 2x)
Remove parenthesis by distributing x 4 + 3x + 2x2
Rewrite the expression in descending order of exponents 2x2 + 3x + 2