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

determine weather the function is linear or quadratic. identify the quadratic, linear-example-1
User Qidong
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1 Answer

14 votes
14 votes

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

User DmitryB
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