Question

Which represents a quadratic function? f(x) = −8x3 − 16x2 − 4x f (x) = three-quarters x 2 + 2x − 5 f(x) = StartFraction 4 Over x squared EndFraction minus StartFraction 2 Over x EndFraction + 1 f(x) = 0x2 − 9x + 7

Answer 1

`2.\ f(x) = (3)/(4)x^2 + 2x - 5`

Explanation:

Given

`f(x) = -8x^3 - 16x^2 - 4x\\f(x) = (3)/(4)x^2 + 2x - 5\\f(x) = (4)/(x^2) - (2)/(x) + 1\\f(x) = 0x^2 - 9x + 7`

Required

Which of the above is a quadratic function

A quadratic function has the following form;

`ax^2 +bx + c = 0 \ where \ a\\eq 0`

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

`1.\ f(x) = -8x^3 - 16x^2 - 4x`

This is not a quadratic function because it follows the form
`f(x) = ax^3 + bx^2 + c` and this is different from
`ax^2 +bx + c = 0 \ where \ a\\eq 0`

`2.\ f(x) = (3)/(4)x^2 + 2x - 5`

This function has an exact match with
`ax^2 +bx + c = 0 \ where \ a\\eq 0`

By comparison;
`a = (3)/(4)\ b = 2\ and\ c = -5`

`3.\ f(x) = (4)/(x^2) - (2)/(x) + 1`

This is not a quadratic function because it follows the form
`f(x) = (a)/(x^2) + (b)/(x) + c` and this is different from
`ax^2 +bx + c = 0 \ where \ a\\eq 0`

`4.\ f(x) = 0x^2 - 9x + 7`

This is not a quadratic function because it follows the form
`f(x) = ax^2 +bx + c = 0\ but\ a = 0`

Unlike the quadratic function where
`a\\eq 0`

So, from the list of given options, only
`2.\ f(x) = (3)/(4)x^2 + 2x - 5` satisfies the given condition