which represents a quadratic function?\n○ (f(x)=-8x^{3}-16x^{2}-4x)\n○ (f(x)=\frac{3}{4}x^{2}+2x - 5)\n○…

Explanation:

Step1: Recall quadratic - function form

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

Step2: Analyze each option

• For $f(x)=-8x^{3}-16x^{2}-4x$, the highest power of $x$ is 3, so it is a cubic function, not quadratic.
• For $f(x)=\frac{3}{4}x^{2}+2x - 5$, here $a = \frac{3}{4}\neq0$, $b = 2$, $c=-5$, and the highest power of $x$ is 2. So it is a quadratic function.
• For $f(x)=\frac{4}{x^{2}}-\frac{2}{x}+1=4x^{-2}-2x^{-1}+1$, the powers of $x$ are negative, so it is not a quadratic function.
• For $f(x)=0x^{2}-9x + 7=-9x + 7$, since $a = 0$, it is a linear function, not quadratic.

Answer:

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