Question

30 POINTSS!!

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

f(x)=f(x)=x3+2x2−x−2
0=x3+2x2−x−2
0=(1)3+2(1)2−(1)−2 −−> 1+2−1−2 −−> =0, so 1 works.
0=(−1+2(−1−1)−2 −> −1+2+1−2 −>0 −−> so,
f(x)=(−2)3+2(−2)2−(−2)−2 −> −8+8+2−2 −> 0 So, −2 also works.
make x=0
f(x)=(0)3+2(0)2−(0)−2 ⇒ 0+0−0−2 ⇒ −2. So y−intercept is −2
the x-intercepts are 1, -1 & -2 OR (1,0) (-1,0) (-2,0) and y intercept is -2 OR (0,-2) then you can graph it.