Question

Which represents a quadratic function? f(x) = −8x3 − 16x2 − 4x f (x) = x 2 + 2x − 5 f(x) = + 1 f(x) = 0x2 − 9x + 7

Answer 1

`\text{A quadratic function:}\ f(x)=ax^2+bx+c\\\\\text{where}\ a\\eq0`

`f(x)+-8x^3-16x^2-4x-NOT\\\\f(x)=x^2+2x-5-YES\\\\f(x)=?+1-NOT\\\\f(x)=0x^2-9x+7-NOT`

Answer 2

`f(x)=x^(2) +2x-5`

Explanation:

We need to find the function
`f(x)` representing a quadratic function.

Now, we know that the general form of a quadratic function is
`ax^(2)+bx+c` , where
`a\\eq 0`

So, Let us consider each function one by one.

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

Clearly, the above function has a cubic term in it so it is a cubic function NOT a quadratic function.

Now,
`f(x)=x^(2) +2x-5`

Clearly, the above function is of the form
`ax^(2)+bx+c` so, it is a quadratic function.

Now,
`f(x)=0x^(2) -9x+7`

Here, the coefficient of
`x^(2)` is 0. So, it is not of the form
`ax^(2)+bx+c` , where
`a\\eq 0` .

So, it is NOT a quadratic function.

Hence, only
`f(x)=x^(2) +2x-5` is a quadratic function among the all functions.