SOLUTION: For the polynomial Function : F(x)=-2(x + 1/2) (x+4)^2 a)List each real zero and its multiplicity: b)Determine whether graph crosses or touches the x-axis at each x-intercept:

Question 1189458: For the polynomial Function : F(x)=-2(x + 1/2) (x+4)^2
a)List each real zero and its multiplicity:
b)Determine whether graph crosses or touches the x-axis at each x-intercept:
c)Determine the behavior of the graph near each x-intercept(zero):
d)Determine the maximum number of turning point on the graph:
e)Determine the end behavior, that is finding the power function that the graph of
f resembles for large values of |x|:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

For the polynomial Function :

a)List each real zero and its multiplicity:

if =>,..... multiplicity 1
if =>,..... multiplicity 2
b)Determine whether graph crosses or touches the x-axis at each x-intercept:

For zeros with multiplicities, the graphs or are tangent to the x-axis at these x-values.
For zeros with multiplicities, the graphs or intersect the x-axis at these x-values.
have an multiplicity => the graph will the x-axis
have an multiplicity=> the graph will the x-axis

c)Determine the behavior of the graph near each x-intercept(zero):
Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is , the degree is , i.e. even, and the leading coefficient is , i.e. negative.
This means that f(x)→ ∞ as x→ -∞ , f(x)→ -∞ as x→ ∞

d)Determine the maximum number of turning point on the graph:
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
This function f is a th degree polynomial function and has turning points.

e)Determine the end behavior, that is finding the power function that the graph of
f resembles for large values of ||:
If we expand we get

..... the dominating term

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