Answer
(a) $x=0$ (multiplicity 1), $x=-\sqrt 3$ (multiplicity 1) and $x=\sqrt 3$ (multiplicity 1).
(b) $x=0, \pm\sqrt 3$ crosses the x-axis.
(c) $2$.
(d) $y=4x^3$.
Work Step by Step
(a) For $f(x)=4x(x^2-3)$, we can list real zero as $x=0$ (multiplicity 1), $x=-\sqrt 3$ (multiplicity 1) and $x=\sqrt 3$ (multiplicity 1).
(b) At $x=0, \pm\sqrt 3$ the graph crosses the x-axis.
(c) The maximum number of turning points on the graph is given by $n-1=3-1=2$.
(d) As $n=3, a_3\gt0$, the end behaviors are rise to the right and fall to the left, similar to $y=4x^3$.
