We want to determine the end behavior of the graph of the given polynomial function. To do so, we will pay close attention to the leading term ax^n, where a is the leading coefficient and n is the degree of the polynomial. Let's consider the given polynomial function. Note that it is already written in standard form.
y= - 2x^4+8x^3+4x^2-3
We can see above that the leading coefficient is - 2 and the degree is 4. Let's now see how the leading coefficient and degree affect the end behavior of the graph of a polynomial function.
Since - 2<0 and 4 is an even number, the end behavior of the given function is down and down. This corresponds to option A.
