Question

Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.f(x)=(3x-4)(-6x+5)

Answer 1

At first glance, it might be tempting to say this is a linear function, because we see linear terms (3x and –6x); however, these are multiplied together, so it's actually a quadratic. 

We need to expand the function (hint: use FOIL) to identify the terms.

$f(x)=(3x-4)(-6x+5)=-18x^2+39x-20$

The x^2-term, or quadratic term, is $-18x^2$. The x-term, or linear term, is $39x$. The number term, or constant term, is –20.