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.
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W(x) is some function that tells you the change in the height x in water height, per time unit , say days.
W(x) = 0, means no change in water height
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.
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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
i guess make the coefficients whatever you want
so after i choose numbers for them just solve it? @DanJS
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)
yaeh let a=1, b=0, c=1, d=0
that should make it easy to solve with those
i meant c = -1, not 1
w(x) = x^3 - x
I got x^3-x @DanJS
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