Ernest's friend Nik is about to be shot out of a cannon. The path he will travel fallows a parabolic arch that can be described by this polynomial. f(x)=-0.05(x^2-26x-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?

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(x^2-26x-120) represents the path coming out of the cannon. If x is the horizontal distance of 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 the zeros, set the function equal to 0, and then factor the polynomial. Start by setting the function equal to zero.

Factor the Polynomial

The polynomial f(x)=x^2-26x-120) is in the form of x^2 +b+c which can be factored as (x+p)(x+q).

5. Next, factor the polynomial x^2-26x-120. To identify the factors, complete the table. Note: This table does not contain all of the factors of -120, but it has enough to let you factor the polynomial.

p q p+q

10 -12

-12 10

30 -4

4 -30

6. Which values of p and q give the correct factors>

7. Factor the polynomial completely: 0=-0.05(x^2-26x-120)

8. Find the roots of the 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 0. Solve for x with the other two factors.

9. Identify the roots.