Question

determine weather the function is linear or quadratic. identify the quadratic, linear and constant terms.

Answer 1

Note that f(x) is the product of two linear terms. So it must be a quadratic function. To find the quadratic term we simply expand the product of both terms. We have that

$f(x)=(3x+3)(5x\text{ -2\rparen}$

If we expand the product we get

$f(x)=15x^2\text{ - 6x+15x - 6=15x}^2+9x\text{ -6}$

we note that this is of the form

$ax^2+bx+c$

where a is the quadratic term, b is the linear term and c is the constant term. By comparison, we can see that the quadratic term is 15, the linear term is 9 and the constant term is -6. All of this criteria are met by the third option. Meaning the third option is the correct one