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Question 1013093: 4.3
Use the given function to answer the questions below
f(x)=-x^4+x^2
a. Use the leading coefficent test to determine the graphs end behavior
b. Find the x-intercepts: x=
c. At which zeros does the graph of the function cross the x-axis:
d. At which zero does the graph of the function touch the x-axis and turn around:
e. Find the y intercept buy computing f(0):
f. Determine the symetry of the graph (odd, even, or neither):
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! Use the given function to answer the questions below
a. Use the leading coefficient test to determine the graphs end behavior
the leading coefficient of  is 
When  (which is  in your case) is  and  is negative (which is in your case),graph  to the left and right
b. Find the x-intercepts:
if  we have double solution 
if  => => => or 
so, the x-intercepts are at:
( ,)
( ,)
(,)
c. At which zeros does the graph of the function cross the x-axis:
the graph of the function cross the x-axis at and
d. At which zero does the graph of the function touch the x-axis and turn around:
at
e. Find the y intercept buy computing f(0):
so, the y-intercept is at:
(,)
f. Determine the symmetry of the graph (odd, even, or neither):
Replace x with −x in order to determine if the function is odd, even, or neither.
The function is .
y-axis is axis of symmetry
see it on a graph:
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