Question

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.

Answer 1

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)

Answer 2

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.

Answer 3

it really helped