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?

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

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