Answer
(a) There aren't any real zeros in this function.
(b) The graph of this function doesn't cross or touch the x-axis at any point.
(c) The maximum number of turning points is 5.
(d) The end behavior resembles $-2x^6$
Work Step by Step
Real zeros (or the x-intercepts) are found by making the function equal to zero and solving for x. This is made easier if the polynomial function is in the factored form $f(x)=a(x-r_1)(x-r_2)...(x-r_n)$ since we can solve all $(x-r)$'s for zero. The multiplicity is determined by the exponent that $(x-r)$ is raised by. For example, $(x-10)$ has a multiplicity of 1 while $(x+2)^3$ has a multiplicity of 3.
The graph touches the x-axis when the multiplicity is even while the graph crosses the x-axis when the multiplicity is odd.
The maximum number of turning points is determined by the highest degree of the function minus 1. For example, the maximum number of turning points of $x^5$ is 5-1=4.
The end behavior resembles the graph of $y=a_nx^n$ where $f(x)= a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$