To begin a football game, a kicker has to kick off. The football follows the path h(x)=−1/30x(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=−1/30x(x−61)


(1 point)
The ball will h

1 answer

To determine how far the football will have traveled when it hits the ground, we need to set the height \( h(x) \) equal to zero and solve for \( x \). The function given is:

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

Setting it equal to zero:

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

To solve this equation, we can multiply both sides by -30 (to eliminate the fraction):

\[ 0 = x(x-61) \]

Now we can factor the equation:

\[ x(x-61) = 0 \]

Setting each factor equal to zero gives us:

  1. \( x = 0 \)
  2. \( x - 61 = 0 \) ⇒ \( x = 61 \)

Thus, the solutions are \( x = 0 \) and \( x = 61 \).

In the context of the football's path, \( x = 0 \) represents the point where the ball is kicked from, and \( x = 61 \) represents the point where the ball hits the ground.

Therefore, the ball will have traveled 61 yards when it hits the ground.