Question

Which represents a quadratic function? F(x)= 2x3+2x2-4

Answer 1

The complete question is:

Which represents a quadratic function?

$f(x)=2x^3+2x^2-4\\ \\ f(x)=-7x^2-x+2\\ \\ f(x)=-3x+2\\ \\ f(x)=0x^2+3x-3$

Answer:

• The second option: - 7x² - x + 2

Explanation:

The polynomial functions are classified according to the degree of the leading term, i.e. the term with the variable raised to the highest exponent.

Thus:

• HIghest exponent 0 ⇒ constant function (degree 0)
• Highest exponent 1 ⇒ linear function (degree 1)
• Highest exponent 2 ⇒ quadratic function (degree 2)
• Highest exponent 3 ⇒ cube function (degree 3)
• Highest exponent 4 ⇒ degree 4

And so on.

Thus the only quadratic function among the expressions given is the second choice:

• $f(x)=-7x^2-x+2$

The first choice is a cube function (the highest exponent is 3), the third choice is a linear function (highest exponent is 1).

The fourth choice is also a linear function because the coefficient of the term with exponent 2 is zero, meaning that this term does not exist.