Question 865756
{{{f(x)=(x+4)^2(x-2)^2}}}


This is already in factored form.  x intercepts are -4 and +2.
y-intercept happens for {{{highlight(f(0))=4^2*2^2=16*4=highlight(64)}}}.


Examine the function factors very carefully.  Each individual binomial factor may be less than, equal to, or greater than zero; but because both factors are squared, f(x) stays POSITIVE, so will always be at or above the horizontal axis.  This means, f(x) NEVER crosses the x axis at any x intercept.


The vertical labeling is imprecise, but here is a fair representation of the graph:
{{{graph(400,400,-7,5,-5,80,(x+4)^2(x-2)^2)}}}