Given the function f (x) = - 2x+3x^2-5, what is the right end behavior

The right-end behaviour of all polynomials is always (i. e. whether highest power is odd or even) increasing when the leading coefficient (coefficient of the highest powered variable) is positive.

Otherwise, it is decreasing.

The leading coefficient is + 3 (i. e. positive), corresponding to the term + 3x^2.