Verify if the function is odd or even? y=17x^3-12x^2

A function is even if f(-x) =
f(x).

In other words, plugging in a number will be the same
as plugging in the negative value of the same number. The function is not
changing.

We'll analyze the given function, replacing each x by
-x.

f(-x) = 17(-x)^3 -
12(-x)^2

We'll compute raising -x to the 3rd and 2nd
powers and we'll get:

(-x)^3 = (-x)(-x)(-x) = x^2*(-x) =
-x^3

f(-x) = -17x^3 - 12x^2

So
we can see that:

f(-x) is not equal to f(x) which means
that the function f(x) is not an even function. 

We'll
check if the function is odd;

f(-x) =
-f(x)

f(-x) = -17x^3 -
12x^2

If we'll factorize by -1 we'll
get:

f(-x) = -(17x^3
+ 12x^2)

The expression inside brackets is not the function
f(x).

The given function is nor odd neither
even function.