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General Form of a Quadratic Expression

A quadratic expression written in the following format is said to be in the general form.
`ax^2 + bx + c`

Characteristics of the general form:

  • `a`, `b` and `c` are numbers
  • `a` does not equal 0
  • `b` and `c` can be equal to 0

Description of the general form:

When a quadratic equation or any algebraic equation is written in descending order of exponents of its variable, it is said to be in the general form.

The above equation can be written as
`ax^2 + bx^1 + cx^0`
Notice that the first term in the general form has an exponent of '2' on `x`, the second term has an exponent of 1 on `x` and the third term has an exponent of 0 on `x`. Thus, in the general form, the terms are written in descending powers of `x`.

Examples

The following quadratic expressions are in the general form:
  • `x^2 + 2x + 1`
  • `10x^2 + 3x + 4`
  • `4x^2 - 8x + 4`
...while the following quadratic equations are not in the general form:
  • `x + 2x^2 + 5`
  • `1 + 3x + 3x^2`
  • `x^2 + 1 + 2x`

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