# 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.

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It's not quadratic becouse it have power that is higher then $2$. Form is quadratic, when the highest power is $2$. – Bartek Pawlik Jun 11 '13 at 20:16
The power $2$ must occur in the polynomial, and it must be the highest power of the variable in the expression. – André Nicolas Jun 11 '13 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.

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Links and all! :-) +1 – Amzoti Jun 12 '13 at 0:27
You're so sweet, @Babak. Yes, I am winding down, preparing for bed. You go get 'em! Kill those questions! – amWhy Jun 13 '13 at 4:57

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

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Your first sentence is correct, if it is a polynomial. – vadim123 Jun 11 '13 at 20:20