For the polynomial function below List each real zero and it

For the polynomial function below: List each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. Determine the maximum number of turning points on the graph. 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)(x+6)_2 Find any real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The real zero(s) off is/are D. There are no real zeros. The multiplicity of the larger zero is D. The multiplicity of the smaller zero is D. The graph the x-axis at the larger x-intercept. The graph the x-axis at the smaller x-intercept. The maximum number of turning points on the graph is D. (Type a whole number.) Type the power function that the graph of f resembles for large values of |x|. y=D

Solution

f(x) = - 2(x-2)(x+6)²

(-2x+4)(x+6)² = 0

-2x + 4 = 0

x = 2

x+6 = 0

x = -6

a)

A ) the real zeroes of f are 2, -6, -6

Multiplicity of larger zero is 1

Multiplicity of smaller zero is 2

b) y = -2(x-2)(x+6)²

x-intercept = 2, -6,-6

The graph crosses the x axis at larger x-intercept

The graph touches the x axis at smaller x- intercept

c) The minimum number of turning points on the graph are 2

d) Type of power function that the graph resembles for large value of x.

f(-x) = -2(-x -2) (-x +6)² = 2(x-2) (-x+6)²

It is odd function

y = 2(x-2) (-x+6)²