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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 to be used in your explanations.

Question

Help Ill give a medal who answers this!  
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 to be used in your explanations.

campbell_st · Answer

to find the x intercepts, let W(x) = 0 and solve for x

here is a really simple example... let 

$$W(x) = -x^2 - 5x + 6$$

let W(x) = 0

so 

$$0 = x^2 + 5x - 6$$

this can be solved by factoring

-(x -3)(x-2) = 0

so x = 2 and x = 3 are the intercepts... 

and the graph looks like 

|dw:1436492163328:dw|