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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2$\begingroup$ It's not quadratic becouse it have power that is higher then $2$. Form is quadratic, when the highest power is $2$. $\endgroup$– Bartek PawlikJun 11, 2013 at 20:16
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2$\begingroup$ The power $2$ must occur in the polynomial, and it must be the highest power of the variable in the expression. $\endgroup$– André NicolasJun 11, 2013 at 20:16
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2 Answers
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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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$\begingroup$ You're so sweet, @Babak. Yes, I am winding down, preparing for bed. You go get 'em! Kill those questions! $\endgroup$– amWhyJun 13, 2013 at 4:57
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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
answered Jun 11, 2013 at 20:16
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1$\begingroup$ Your first sentence is correct, if it is a polynomial. $\endgroup$– vadim123Jun 11, 2013 at 20:20