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

1.The distance between the cannon and the ground is represented by f(x).

2. When f(x) = 0, there will be two 'x' values. The point where the graph crosses the positive x-axis represents the point where the cannon hits the earth.

3.It would, absolutely. We may position the net at the spot where the cannon will hit the ground if we know where the cannon will hit the earth.

4f(x) = 0

-0.05 (x² - 26x -120) = 0

x² - 26x - 120 = 0

Step-by-step explanation:

Answer 2

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