Question

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.

Answer 1

B. It cant be A because a negative leading coefficient would mean it was turned facing down. It can't be C because the bottom of the loop is a turning point. It cant be C because it doesn't cross the x-axis.

Answer 2

Answer:

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.