which represents a quadratic function?\n$f(x)=-8x^{3}-16x^{2}-4x$\n$f(x)=\\frac{3}{4}x^{2}+2x…

which represents a quadratic function?\n$f(x)=-8x^{3}-16x^{2}-4x$\n$f(x)=\\frac{3}{4}x^{2}+2x - 5$\n$f(x)=\\frac{4}{x^{2}}-\\frac{2}{x}+1$\n$f(x)=0x^{2}-9x + 7$

which represents a quadratic function?\n$f(x)=-8x^{3}-16x^{2}-4x$\n$f(x)=\\frac{3}{4}x^{2}+2x - 5$\n$f(x)=\\frac{4}{x^{2}}-\\frac{2}{x}+1$\n$f(x)=0x^{2}-9x + 7$

Answer

Explanation:

Step1: Recall the definition of a quadratic function

A quadratic function is of the form (f(x)=ax^{2}+bx + c), where (a\neq0), (b), and (c) are constants.

Step2: Analyze each option

  • For (f(x)=-8x^{3}-16x^{2}-4x), the highest - degree term is (x^{3}) (degree (3)), so it is a cubic function.
  • For (f(x)=\frac{3}{4}x^{2}+2x - 5), it is in the form (ax^{2}+bx + c) with (a=\frac{3}{4}\neq0), (b = 2), (c=-5).
  • For (f(x)=\frac{4}{x^{2}}-\frac{2}{x}+1=4x^{-2}-2x^{-1}+1), the exponents of (x) are (-2) and (-1), which does not match the form of a quadratic function ((ax^{2}+bx + c)).
  • For (f(x)=0x^{2}-9x + 7=-9x + 7) (since (0x^{2}=0) for all (x)), it is a linear function ((y = mx + b) with (m=-9) and (b = 7)).

Answer:

(f(x)=\frac{3}{4}x^{2}+2x - 5)