A quadratic function is a function where the highest degree is 2. That means there must be a variable in the quadratic function raised to the second power, and that variable can't be raised to a higher power.
For example:
[tex]f(x) = x^{2} + 2x + 3\\
f(x) = 3x^{2} + 2\\
f(x) = 5 x^{2} + 5x + 7
[/tex]
are all quadratic functions because the variable, x, is raised to the second power and it's the highest power in the function. The variables can be multiplied by constants.
On the other hand, [tex] x^{3} + 2x^{2} + 4x + 5[/tex], for example, isn't a quadratic function because x is being raised to the 3rd power, and you can't have a power higher than 2.
You'll often see quadratics in the form [tex]ax^{2} + bx +c[/tex], where a, b, and c are constants.
