Word Problems

Question

a projectile follows a parabolic path whose height, in meters, is given by the function f(x)=-x squared +2x+2. Find the maximum horizontal distance that the projectile may cover.

Answer 1

The horizontal distance is the distance between the two x-intercepts, f(x) = 0.

 

0 = -x² + 2x + 2          Completing the square

0 = -(x² - 2x    ) +2

0 = -(x² - 2x + 1) + 2 + 1

0 = -(x - 1)² + 3

-3 = -(x - 1)²

3 = (x - 1)²

±√3 = x - 1

1 ± √3 = x

 

The distance between these to x values is 2(1 + √3), or 2 + 2√3.