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

$\text{A quadratic function:}\ f(x)=ax^2+bx+c\\\\\text{where}\ a\neq0$
$f(x)+-8x^3-16x^2-4x-NOT\\\\f(x)=x^2+2x-5-YES\\\\f(x)=?+1-NOT\\\\f(x)=0x^2-9x+7-NOT$

Answer 2

Answer:

$f(x)=x^{2} +2x-5$

Step-by-step 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 $a\neq 0$

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 $a\neq 0$ .

So, it is NOT a quadratic function.

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