Question

"Sketch a possible graph for a negative Quintic polynomial with one real zero." Can anyone explain how this is done? And if possible provide a graph?

Answer 1

quintic means degree of 5.

a negative quintic would be: f(x) = -x⁵ +              

an example with one real zero could be: -x⁵ + x³ + x + 3   (see attachment)

Answer 2

Well let's start with y = -x^5 and y = - x^5 +1

The graph looks like the one on the right for these two.  The red one is y = - x^5 and the blue one is y = - x^5 + 1

See below on the right

You can tell that these two are correct because there is only 1 x axis intercept for each of them.  That means there is only 1 real solution which is what you are calling for.

Another one could be something like

y = -(x - 5)(x^2 + 2)(x^2 + 3)

The graph of that is on the left.