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

W(x) is some function that tells you the change in the height x in water height, per time unit , say days.

Answer 2

W(x) = 0, means no change in water height

Answer 3

So how do you 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. @DanJS im not good at math at all so if you dont mind please break it down for me.

Answer 4

polynomial degree 3, highest power on x

w(x) = a*x^3 + b*x^2 + c*x +d

a,b,c and d are coefficients, and d is the value initially when the graph starts at x=0

Answer 5

i guess make the coefficients whatever you want

Answer 6

so after i choose numbers for them just solve it? @DanJS

Answer 7

yeah, the x-intercepts are when it crosses the xaxis, and y=0

solve for the times x when that happens
w(x) = 0



to graph , you can use those x-intercepts and pick a point or 2 in between them too, pick x value solve for w(x)

Answer 8

yaeh let a=1, b=0, c=1, d=0

that should make it easy to solve with those

Answer 9

i meant c = -1, not 1

w(x) = x^3 - x
=x*(x^2-1)
=x* (x+1)*(x-1)

Answer 10

I got x^3-x @DanJS

Answer 11

w(x) = 0 when x= 0 or x=1 or x=-1

it says to just describe how to make the graph
you can plot those 3 x-intercept points

maybe pick some values for x in between those points and figure w(x),
x=-2, x=-1/2, x=1/2 , x = 2

Answer 12

okay.