Answer
(a) $x=-4$ (multiplicity 1) and $x=-3$ (multiplicity 3).
(b) $x=-4$ and $x=-3$ cross the x-axis.
(c) $3$.
(d) $y=4x^4$.
Work Step by Step
(a) For $f(x)=4(x+4)(x+3)^3$, we can list real zero as $x=-4$ (multiplicity 1) and $x=-3$ (multiplicity 3).
(b) At $x=-4$ and $x=-3$ the graph crosses the x-axis.
(c) The maximum number of turning points on the graph is given by $n-1=4-1=3$.
(d) As $n=4, a_4\gt0$, the end behaviors are rise to the right and rise to the left similar to $y=4x^4$.
