Question

Which of the following notations correctly describe the end behavior of the polynomial graphed below?

Answer 1

The right answer is C

Let me to explain. From the graph we know that the vertex of this parabola is $V(0,8)$. This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative. Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right. In a mathematical language this is:

$x \rightarrow -\infty, f(x) \rightarrow -\infty \\ \\ x \rightarrow \infty, f(x) \rightarrow -\infty$