If f (x) = ax ^ 2 + BX ^ 2 + C is even function, then f (x) = ax ^ 3 + BX ^ 2 + CX is even function Given that the function f (x) = ax ^ 2 + BX ^ 2 + C (a is not equal to zero) is even, then f (x) = ax ^ 3 + BX ^ 2 + CX is () A. Odd function B. even function C. both odd and even function D. non odd and non even function And why?

If f (x) = ax ^ 2 + BX ^ 2 + C is even function, then f (x) = ax ^ 3 + BX ^ 2 + CX is even function Given that the function f (x) = ax ^ 2 + BX ^ 2 + C (a is not equal to zero) is even, then f (x) = ax ^ 3 + BX ^ 2 + CX is () A. Odd function B. even function C. both odd and even function D. non odd and non even function And why?

Odd function
First of all, a is not equal to 0, including odd polynomials, which will not be even (this is the original source of the name of odd and even functions, please remember)
The quadratic function is even, so it is symmetric about the y-axis, that is, x = 0, and the symmetric axis is x = - B / 2a, so B = 0
The rest f (x) = ax ^ 3 + CX are odd polynomials, choose a