SOLUTION: 4.3 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 grap

Algebra ->  Functions -> SOLUTION: 4.3 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 grap      Log On


   

Question 1013834: 4.3
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)
b.Find the x-intercepts. X=
c.At which zeros does the graph of the function cross the x-axis? X=
d.At which zeros does the graph of the function touch the x-axis and turn around? X=
e. Find the y-intercept by computing f(0). f(0)=
f. What is the symmetry of the graph?
g. Determine the graph of the function:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Use the given function to answer the questions that follow
f%28x%29+=-x%5E4+%2B36x%5E2
a.Use the Leading Coefficent Test to determine the graphs end behavior. (How does the graph rise or fall)
the Leading Coefficient is a%5Bn%5D%5En=-x%5E4 (but all we need is the "minus" part of the leading coefficient),when n=4 is even and a%5Bn%5D is negative graph highlight%28falls%29 to the left and right


b.Find the x-intercepts.
0+=-x%5E4+%2B36x%5E2
0+=-x%5E2%28x%5E2+-36%29
if 0+=-x%5E2=>highlight%28x=0%29(multiplicity 2)
if 0+=%28x%5E2+-36%29=>x%5E2=36=>x=sqrt%2836%29=>highlight%28x=6%29 or highlight%28x=-6%29

c.At which zeros does the graph of the function cross the x-axis?
at highlight%28x=6%29 or highlight%28x=-6%29

d.At which zeros does the graph of the function touch the x-axis and turn around?
at highlight%28x=0%29

e. Find the y-intercept by computing f(0).
f%280%29=-0%5E4+%2B36%2A0%5E2
f%280%29=-0+%2B0
f%280%29=0
the y-intercept is at origin

f. What is the symmetry of the graph?
y-axis

g. Determine the graph of the function: