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Edufirst

The complete question is:

Which represents a quadratic function?

[tex]f(x)=2x^3+2x^2-4\\ \\ f(x)=-7x^2-x+2\\ \\ f(x)=-3x+2\\ \\ f(x)=0x^2+3x-3[/tex]

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:

  • [tex]f(x)=-7x^2-x+2[/tex]

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.

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