Answer
(a) $x=7$ (multiplicity 1) and $x=-3$ (multiplicity 2).
(b) $x=7$ crosses the x-axis, $x=-3$ touches the x-axis.
(c) $2$.
(d) $y=3x^3$.
Work Step by Step
(a) For $f(x)=3(x-7)(x+3)^2$, we can list real zero as $x=7$ (multiplicity 1) and $x=-3$ (multiplicity 2).
(b) At $x=7$ the graph crosses the x-axis, while at $x=-3$ the graph touches the x-axis.
(c) The maximum number of turning points on the graph is given by $n-1=3-1=2$.
(d) As $n=3, a\gt0$, the end behaviors are rise to the right and fall to the left similar to $y=3x^3$.