Question 1013834
Use the given function to answer the questions that follow

{{{f(x) =-x^4 +36x^2}}}

a.Use the Leading Coefficent Test to determine the graphs end behavior. (How does the graph rise or fall)

the Leading Coefficient is {{{a[n]^n=-x^4}}} (but all we need is the "minus" part of the leading coefficient),when {{{n=4}}} is {{{even}}} and {{{a[n]}}} is {{{negative}}} graph {{{highlight(falls)}}} to the {{{left}}} and {{{right}}} 



b.Find the x-intercepts. 

{{{0 =-x^4 +36x^2}}}

{{{0 =-x^2(x^2 -36)}}}

if {{{0 =-x^2}}}=>{{{highlight(x=0)}}}(multiplicity {{{2}}})

if {{{0 =(x^2 -36)}}}=>{{{x^2=36}}}=>{{{x=sqrt(36)}}}=>{{{highlight(x=6)}}} or {{{highlight(x=-6)}}}


c.At which zeros does the graph of the function cross the x-axis? 

at {{{highlight(x=6)}}} or {{{highlight(x=-6)}}}


d.At which zeros does the graph of the function touch the x-axis and turn around? 

at {{{highlight(x=0)}}}


e. Find the y-intercept by computing f(0). 

{{{f(0)=-0^4 +36*0^2}}}

{{{f(0)=-0 +0}}}

{{{f(0)=0}}}

the y-intercept is at origin


f. What is the symmetry of the graph?

y-axis


g. Determine the graph of the function: 


{{{drawing( 600,600,-10,10,-150,350,
circle(0,0,.12),locate(0,12,p(0,0)),
circle(-6,0,.12),locate(-6,12,p(-6,0)),
circle(6,0,.12),locate(6,12,p(6,0)),
 graph( 600,600,-10,10,-150,350,-x^4 +36x^2)) }}}