Question 849554
you can find the equation from the roots.
the roots are:
x = 0
x = 2
x = 5
x = -4
x = -4
multiplying all those together and I got:
x^5 + x^4 - 30x^3 - 32x^2 + 160x
i then graphed that equation.
that graph looked like the picture, but was oriented in revedrse, so i multiplied it by -1 and got:
-x^5 + x^4 + 30x^3 + 32x^2 - 160x
that graph was oriented right but the point (1,-5) was not on the graph.
instead i got the point (1,-100).
this was much to low, so i divided the equation by 20 and got:
-.05x^5 + .05x^4 + 1.5x^3 + 1.6x^2 - 8x
that allowed the point (1,-5) to be on the graph and kept all the roots where they were supposed to be.
the graph looks like this:
{{{graph(600,600,-10,10,-10,30,-.05*x^5 - .05*x^4 + 1.5*x^3 + 1.6*x^2 - 8x)}}}
it is a 5th degree equation.
the coefficient of the leading term had to be negative, so it start high on the left and ends low on the right.
the multiplicity at x = -4 is even (2 roots at x = -4).  
the point (1,-5) is on the graph.