Which graph shows a polynomial function with a positive leading coefficient?

B

Step-by-step explanation:

It isn't A. A has to be something like y = -x^2  That minus sign directs the parabola downward.

It could be B which is something like y =  x^3 - 5

C has an odd number of real roots (5). In other words it crosses the x axis 5 times. So let's make one of these up and graph it

y = (x^2 - 4)(x^2 - 1)(x + 3) Study this for a minute. The leading coefficient of this polynomial is plus 1. There are no negatives in front of the x. The highest degree is x^5. Now here's the key question: on the left side where does the graph start? In Quad three right? It's coming from the lower left. That is exactly what graph C is NOT doing.  So for C the graph has a leading coefficient that is less than 0.   a<0

Not C.

D is not the answer either. It opens downward and looks like it is something like y = - x^4 + 3x^3 - 2x^2 + 5x - 2

Answer B: