Solved Examples: Identifying Quadratic Expressions

Identify whether the following expressions are quadratic or not, and state why or why not they are quadratic:

`x^2 + 2x^3 + 3`

This expression is not quadratic because it contains a term with exponent greater than 2 on the variable `x`.

`x + 2`

This expression is not quadratic because it does not contain a term with exponent '2' on the variable.

`x^2 + 2x + 1`

This expression is quadratic because 

1. the greatest exponent on `x` is 2
2. `x` does not have negative exponents or exponents greater than 2

`xy + x^2 + y^2`

The above expression is quadratic because its degree is 2. In other words, it is quadratic because the sum of exponents of `x` and `y` in any single term is never greater than 2.

`x^2y + xy + 1`

This expression is not quadratic because the sum of exponents of `x` and `y` in the first term is 3.