SOLUTION: Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. f(x) = -x^3(x + 2)^2(x - 6) origin symmetry y-axis symmetry nei

Algebra ->  Finance -> SOLUTION: Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. f(x) = -x^3(x + 2)^2(x - 6) origin symmetry y-axis symmetry nei      Log On


   

Question 1086965: Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
f(x) = -x^3(x + 2)^2(x - 6)

origin symmetry

y-axis symmetry

neither
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+-x%5E3%28x+%2B+2%29%5E2%28x+-+6%29

the graph will be symmetrical with respect to the y-axis if:
f%28-x%29+=+f%28x%29
check:
f%28-x%29+=+f%28x%29......if x=1
f%28-1%29+=+f%281%29
+%28-%28-1%29%5E3%29%28-1+%2B+2%29%5E2%28-1-6%29=-1%5E3%281+%2B+2%29%5E2%281-6%29
+-%28-1%29%281%29%5E2%28-7%29=-1%283%29%5E2%28+-5%29
+1%281%29%28-7%29=-1%289%29%28+-+5%29
+-7%3C%3E45=>the graph is not symmetrical with respect to the y-axis


the graph will be symmetrical with respect to the origin if:


f%28-x%29+=+-f%28x%29......if x=1
f%28-1%29+=+f%281%29
+-%28-1%29%5E3%28-1+%2B+2%29%5E2%28-1+-+6%29=-1%5E3%281+%2B+2%29%5E2%281+-+6%29
+-%28-1%29%281%29%5E2%28-7%29=-%28-1%283%29%5E2%28+-+5%29%29
+1%281%29%28-7%29=-%28-1%289%29%28+-+5%29%29
+-7%3C%3E-45=>the graph is not symmetrical with respect to the origin



answer: neither