Answer:
[tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = -8x^3 - 16x^2 - 4x\\f(x) = \frac{3}{4}x^2 + 2x - 5\\f(x) = \frac{4}{x^2} - \frac{2}{x} + 1\\f(x) = 0x^2 - 9x + 7[/tex]
Required
Which of the above is a quadratic function
A quadratic function has the following form;
[tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
So, to get a quadratic function from the list of given options, we simply perform a comparative test of each function with the form of a quadratic function
[tex]1.\ f(x) = -8x^3 - 16x^2 - 4x[/tex]
This is not a quadratic function because it follows the form [tex]f(x) = ax^3 + bx^2 + c[/tex] and this is different from [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
[tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex]
This function has an exact match with [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
By comparison; [tex]a = \frac{3}{4}\ b = 2\ and\ c = -5[/tex]
[tex]3.\ f(x) = \frac{4}{x^2} - \frac{2}{x} + 1[/tex]
This is not a quadratic function because it follows the form [tex]f(x) = \frac{a}{x^2} + \frac{b}{x} + c[/tex] and this is different from [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]
[tex]4.\ f(x) = 0x^2 - 9x + 7[/tex]
This is not a quadratic function because it follows the form [tex]f(x) = ax^2 +bx + c = 0\ but\ a = 0[/tex]
Unlike the quadratic function where [tex]a\neq 0[/tex]
So, from the list of given options, only [tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex] satisfies the given condition
