Posted by **Rachal** on Friday, February 4, 2011 at 5:58pm.

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**, Friday, February 4, 2011 at 6:15pm
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**, Friday, February 4, 2011 at 6:24pm
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**, Wednesday, June 1, 2011 at 6:02pm
af

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