Which of the following describes the polynomial function?
a. the function has a negative leading coefficient.
b. the function has an even degree.
c. the function has zero turning points.
d. the function has one x-intercept.

B. The function has an even degree.

Step-by-step explanation:

A. The function has a negative leading coefficient.

When a function has negative leading coefficient, then it opens downward.

But in this case the graph is opened upwards.

B. The function has an even degree.

As the graph is symmetric about y axis, so the value of f(x) at both x and -x will be same. (for any x and -x, the value of y is same.)

And in even functions f(x)=f(-x), so this graph has even degree function.

C. The function has zero turning points.

Turning point is where f(x) changes it sign. In this case f(x) changes from -ve to +ve at x=2, so it has one turning point.

D. The function has one x-intercept.

x-intercept is where the graph intersects x-axis. In this case the graph doesn't even touch the x axis, so it doesn't have any x-intercept.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i