Question 1188405


{{{f(x)=-(x+3)(x-1)^2(x+1)}}}

{{{f(x) = -x^4 - 2 x^3 + 4 x^2 + 2 x - 3}}}

Describe or determine the following

a. leading term____{{{-x^4}}}_____

b. behavior of the graph_________

Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is {{{-x^4}}}, the degree is {{{4}}}, i.e. {{{even}}}, and the leading coefficient is {{{-1}}}, i.e. {{{negative}}}.
This means that {{{f(x)}}}→-∞ as {{{x}}}→-∞, {{{f(x)}}}→-∞ as {{{x}}}→∞.


c. x-intercept_________

{{{0=-(x+3)(x-1)^2(x+1)}}}=> x-intercepts are {{{x=-3}}}, {{{x=-1}}}, {{{x=1}}}


d. multiplicity of roots___________

{{{x=-3}}} multiplicity  {{{1}}}
{{{x=-1}}} multiplicity {{{1}}}
{{{x=1}}} multiplicity {{{ 2}}}

e. y- intercept________

{{{y=-(x+3)(x-1)^2(x+1)}}} if {{{x=0}}}
{{{y=-(0+3)(0-1)^2(0+1)}}}
{{{y=-3}}}

y- intercept___{{{-3}}}_____

g. Sketch the graph___________



{{{ graph( 600, 600, -10, 10, -10, 10, -(x+3)(x-1)^2(x+1)) }}}