Graph this equation.

Question

Graph the equation f(x)=-x(3-x)(x-2)^2(x+4)^3

Answer 1

It's a 7th degree polynomial with potentially 6 turning points

It has x intercepts at x=0, 3, 2 and -4 Just set each factor =0 and solve for x

the graph doesn't intersect the x axis at 2 and -4, but just touches it at 2 and -4, without crossing the x axis

as x approaches infinity, f(x) approaches negative infinity

as x approaches negative infinity, f(x) approaches positive infinity