I AWARD MEDALS!!
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

I AWARD MEDALS!!
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.

anonymous · Answer

can you explain to me how to do this please?

solomonzelman · Answer

Are you dealing with cubic or quadratic function?

solomonzelman · Answer

the x intercepts of the function is what is asked by the "zeros of the function"
The degreee decides the number of zero, (or x-intercepts)

What ever the function is, when finding x intercepts, set the function equal zero, like$$instead~~~f(x)=.....~~~i t~~~will~~~be~~~0=....~~~~~\And~~~solve~~~for~~~x$$

solomonzelman · Answer

@klorainewilliams, do you need cubic quadratic function, or what?

solomonzelman · Answer

I think cubic, because it says polynomial function.

anonymous · Answer

I think cubric

anonymous · Answer

Sorry I had  to leave the room to help my little sister with something

solomonzelman · Answer

$$~~I~~am~~making~~\it~~up.~~~~~f(x)=f (x) = x^3 + 2x^2 - x - 2$$

solomonzelman · Answer

the possible roots are going to be +-1, +-2
Plug them in to see which of them work.

solomonzelman · Answer

$$set~~\it~~equal~~zero,~~like~~this~~0=x^3+2x^2-x-2$$

solomonzelman · Answer

$$0=(1)^3+2(1)^2-(1)-2~~-->~~1+2-1-2~~-->~~=0,~so~~~1~~works.$$

anonymous · Answer

so like I could use W(x)=5x^3+2x^2+4x+6

solomonzelman · Answer

$$0 = (-1)^3+2(-1)^2-(-1)-2~~~->~~-1+2+1-2~~->0~~~-->~~~so,~~-1~~works$$

solomonzelman · Answer

Just lets do my example I'll show you, OK?

solomonzelman · Answer

One more root.

anonymous · Answer

okay :-)

solomonzelman · Answer

$$f(x)=(-2)^3+2(-2)^2-(-2)-2~~~->~~-8+8+2-2~~~->~0~~~So,~~-2~~also~~works.$$

solomonzelman · Answer

Now lets find the y-intercept.

solomonzelman · Answer

make x=0

anonymous · Answer

okay

solomonzelman · Answer

$$f(x)=(0)^3+2(0)^2-(0)-2~~⇒~~0+0-0-2~~⇒~~-2.~~~So~~y-intercept~~is~~~-2$$

solomonzelman · Answer

-2

anonymous · Answer

oh okay so then our point is (-2, -2)?

solomonzelman · Answer

Knowing that the x-intercepts are
1,  -1  &  -2   OR  (1,0)  (-1,0)  (-2,0)
and 
y intercept is -2   OR  (0,-2)

then e can graph it.

anonymous · Answer

oh okay!

solomonzelman · Answer

|dw:1385223376591:dw|