# What is the defining characteristic of a quadratic function?

I'm helping a high school student prepare for an exam, and I'm unsure how to answer this...

Why is $x^3+2x^2$ not quadratic? I thought anything that had a power of 2 was quadratic.

• It's not quadratic becouse it have power that is higher then $2$. Form is quadratic, when the highest power is $2$. Jun 11, 2013 at 20:16
• The power $2$ must occur in the polynomial, and it must be the highest power of the variable in the expression. Jun 11, 2013 at 20:16

A quadratic must be a polynomial and it must be of degree $2$.
The degree of a polynomial in $x$ is the highest power of $x$ appearing in the function.
So we have that your function is a degree $3$ polynomial, also known as a cubic.
It only depends on the highest order term. In your case, it is a third order polynomial. If it were just $ax^2+bx+c$ it would be quadratic