Question

Ernest's friend Nik is about to be shot out of a connon. 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?

Answer 1

Simplifying

F(x) = -0.05(x2 + -26x + -120)

Multiply F * x

xF = -0.05(x2 + -26x + -120)

Reorder the terms:

xF = -0.05(-120 + -26x + x2)

xF = (-120 * -0.05 + -26x * -0.05 + x2 * -0.05)

xF = (6 + 1.3x + -0.05x2)

Solving

xF = 6 + 1.3x + -0.05x2

Reorder the terms:

-6 + -1.3x + xF + 0.05x2 = 6 + 1.3x + -0.05x2 + -6 + -1.3x + 0.05x2

-6 + -1.3x + xF + 0.05x2 = 6 + -6 + 1.3x + -1.3x + -0.05x2 + 0.05x2

Combine like terms:

6 + -6 = 0

-6 + -1.3x + xF + 0.05x2 = 0 + 1.3x + -1.3x + -0.05x2 + 0.05x2

-6 + -1.3x + xF + 0.05x2 = 1.3x + -1.3x + -0.05x2 + 0.05x2

1.3x + -1.3x = 0.0

-6 + -1.3x + xF + 0.05x2 = 0.0 + -0.05x2 + 0.05x2

-6 + -1.3x + xF + 0.05x2 = -0.05x2 + 0.05x2

-0.05x2 + 0.05x2 = 0.00

-6 + -1.3x + xF + 0.05x2 = 0.00