TONS OF POINTS - please help
The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will
travel follows a parabolic arch that can be described by this polynomial.
f(x) = -0.05(x2-26x-120)
He is supposed to land on a safety net 30 feet away. Does the function give you
enough information to tell you where he will land? If so, how far from the cannon will he land?
Make Sense of the Problem
3 points: 1 point for each answer.
-What do you know?
-What do you want to find out?
-What kind of answer do you expect?
1. The function f(x)=-0.05(x2-26x-120)
Represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent
2.what do the zeros of this function represent? Remember the zeros are where f(x)=0
3. Will the zeros tell you where the net should be placed? Why or why not?
4.to find zeros, set the function equal to 0, and then factor the polynomial start by setting the function equal to 0
5. Next factor the polynomial x2-26x-120. To identify the factors, complete the table: note this does not contain all the factors of -120, but it has enough to let you factor the polynomial
(I tried to type out the table )
pqp+q
P. q. p. |
————————— |
10. | 12 | blank. |
—————————.|
-10 | 12 |. Blank. |
—————————.|
30. |. -4. |. Blank. |
—————————-|
4. |. 30. | blank. |
—————————.|
6. Which values of p and w give the correct factors
7. Factor the polynomial completely
0=-0.05(x2 - 26x -120)
8. Find the roots of equation by setting each factor equal to 0 and solving for x.
Hint: there are three factors, but the constant factor, -0.05, does not equal zero
Solve for x with the other two factors
9. Identify the roots