To begin a football game, a kicker has to kick off. The football follows the path h(x) = - 1/30 * x(x - 61) where h(x) is the height of the football and x is the horizontal distance it has traveled in yards. Solve the equation to determine how far the ball will have traveled when it hits the ground 0 = - 1/30 * x(x - 61) (1 point) The ball will have traveledyards before hitting the ground

Answer 1

To determine how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \). The equation given is:

\[ 0 = -\frac{1}{30} x(x - 61) \]

To find the points where the ball hits the ground, we can set the equation inside the parentheses to zero:

\[ -\frac{1}{30} x(x - 61) = 0 \]

Now, we can solve for \( x \):

1. The product \( x(x - 61) = 0 \) gives us two solutions:
   • \( x = 0 \)
   • \( x - 61 = 0 \) which leads to \( x = 61 \)

Thus, the points at which the height \( h(x) = 0 \) are \( x = 0 \) yards (when the ball is just kicked) and \( x = 61 \) yards (when the ball hits the ground).

Therefore, the ball will have traveled 61 yards before hitting the ground.