Answer
(a) zeros $x=7$ (multiplicity 1) and $x=-3$ (multiplicity 2) .
(b) crosses the x-axis at $x=7$, touches the x-axis at $x=-3$.
(c) $2$.
(d) $y=3x^3$.
Work Step by Step
(a) Given $f(x)=3(x-7)(x+3)^2$, we can find zeros $x=7$ (multiplicity 1) and $x=-3$ (multiplicity 2) .
(b) The graph crosses the x-axis at $x=7$, touches the x-axis at $x=-3$.
(c) The maximum number of turning points on the graph is $n-1=3-1=2$.
(d) The end behavior is similar to those of $y=3x^3$.
