Question

The change in water level of a lake is modeled by a polynomial function, W(x). Describe how to find the x-intercepts of W(x) and how to construct a rough graph of W(x) so that the Parks Department can predict when there will be no change in the water level. You may create a sample polynomial of degree 3 or higher to use in your explanations.

Answer 1

ets say in this case x is the amount or rainfall in inches on a given day. We imagine that the ground around the lake absorbs some amount of rainfall. When rainfall is less than this the lake level does not go up. Lets say that rainfall level is 1 inch so we want the polynomial to equal zero for x = 1 and to increase after that. 

The polynomial y (water level) = (x-1)(x+1) has a solution y = 0 at x = 1 and is an upward facing parabola so that as x increases so does y. negative values of rainfall have no meaning so we are interested only in the polynomial when x is GT zero. 

x=0 y=-1 lake level drops one inch a day without rain 

x=1 y=0 one inch of rain and water level stays constant 

x=2 y = 3 two inches of rain and water level goes up 3 inches