Question 167060
{{{ graph( 300, 300, -10, 10, -100, 100, -2x^3 +6x^2 + 18x -54) }}}
a) X-intercepts 
Looks like x=3 and x=-3 are intercepts.
Plug those values into the equation and check.
{{{f(-3)=-2(-3)^3 +6(-3)^2 + 18(-3) -54}}}
{{{f(-3)=54+54-54-54=0}}}
{{{f(3)=-2(3)^3 +6(3)^2 + 18(3) -54}}}
{{{f(3)=-54+54+54-54=0}}}
Yes, x=3 and x=-3 are the x-intercepts.
Y-intercept: Set x=0.
{{{f(0)=-2(0)^3 +6(0)^2 + 18(0) -54}}}
{{{f(0)=-54}}}
The y intercept is y=-54.
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b) Looks like a relative maxima at x=3, y=0.
Also, looks like a relative minima at x=-1,y=2+6-18-54=-64.
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c) Intersection with what?