For the polynomial function below, answer parts (a) through (d)

Question

(A)list each real zero and it’s multiplicity

(b)determine whether the graph crosses or touches the x-axis at each x-intercept

(c)determine the maximum number of turning points on the graph

(d)determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|

f(x)=2(x^2+7)(x^2+3)^2

Answer 1

(A) there are no real zeros.

the zeros are +or- i*Sqrt(7) and +or- i * sqrt(3) <--- which has multiplicity 2

(B) The graph does not cross or even touch the x-axis. F(0) = 126. Sampling other values

of x shows that this function is always positive. Squaring any number results in positive values. Since nothing is being subtracted, the function must be positive.

(c) since there are no sign changes, there can only be one turning point at most

(d) the function approaches infinity for x --> infinity and x--> negative infinity