Posted by Rachal on .
Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph.
I really need help with this one but I can't post the graph.

Algebra 
Damon,
wherever it crosses the x axis is a zero so
(x  xcrossing ) is a factor
If it gets near the x axis but goes horizontal and veers away again, that is a complex root pair.
like
y = x^2 + 2 x + 4
zeros at
x = [ 2 +/sqrt (4  16)]/2
x = 1 +/ (1/2)sqrt (12)
= 1 +/ i sqrt 3
where would that be horizontal (extrema)?
0 = 2x + 2
x = 1 at extrema (sure enough) 
Algebra 
Damon,
if it goes big +y for both big plus and minus x, then the first term is a x^even power
if it is big minus for x and big Plus for +x (or vice versa for  coefficient)then first term is x^odd power. 
Algebra 
Anonymous,
af