Find the zeros and $y$-intercepts of the following polynomials. Select all statements that can be used to describe the long-run behavior for each.

a) $y=-3 x^2 + 24 x$

Zeros:

A. $(-3,0)$
B. $(0,0)$
C. $(8,0)$
D. $(24,0)$

$y$-intercept: $($ , $)$
Long-run behavior:

A. As $x$ goes to positive infinity, the $y$-values of the polynomial also go to positive infinity.
B. As $x$ goes to positive infinity, the $y$-values of the polynomial go to negative infinity.
C. As $x$ goes to negative infinity, the $y$-values of the polynomial go to positive infinity.
D. As $x$ goes to negative infinity, the $y$-values of the polynomial also go to negative infinity.

b) $y=4 x^2 - 49$

Zeros:

A. $(-3.5,0)$
B. $(3.5,0)$
C. $(4,0)$
D. $(-49,0)$

$y$-intercept: $($ , $)$
Long-run behavior:

A. As $x$ goes to negative infinity, the $y$-values of the polynomial go to positive infinity.
B. As $x$ goes to positive infinity, the $y$-values of the polynomial also go to positive infinity.
C. As $x$ goes to positive infinity, the $y$-values of the polynomial go to negative infinity.
D. As $x$ goes to negative infinity, the $y$-values of the polynomial also go to negative infinity.

Hint: