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.
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)
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.
it really helped

Related Questions

Let W be the set of all polynomials p(t) in P3 such that p(0)=0. Show that W is a subsapce of P3 and... Hoa wants to factor the polynomial P(x)=x5−5x4−23x3+55x2+226x+154. She finds three roots of P(x), −1... how many terms does the polynomial 1/9 + x^2 have? factoring the following polynomial expression completely: 2x^3+x^2-8x-4 If 3−7–√ is a polynomial root, name another root of the polynomial. You want to factor this polynomial. What is the greatest common factor (GCF) ? 6x6y3 + 12x3y5 (1... You want to factor this polynomial. What is the greatest common factor (GCF) ? 6x^6y6^3 + 12x^3y^5 (... Use the equation of the polynomial function ​f(x)equals4 x Superscript 4 Baseline minus x to complet... Use the equation of the polynomial function ​f(x)equalsnegative left parenthesis x minus 4 right par... Use the graph of the polynomial equation y=x^4-10x^2+16 to describe its concavity. How many po...