Question

To begin a football game, a kicker has to kick off. The football follows the path h(x)=−130x(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=−130x(x−61)(1 point)The ball will have traveled_____yards 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 \( h(x) = 0 \), which is given as:

\[ 0 = -130x(x - 61) \]

This equation can be factored into two parts:

1. \(-130x = 0\)
2. \((x - 61) = 0\)

Now let's solve each part:

1. From \(-130x = 0\): \[ x = 0 \] This represents the starting point of the kick-off.

2. From \((x - 61) = 0\): \[ x = 61 \] This represents the point where the ball hits the ground.

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

So the final answer is: The ball will have traveled 61 yards before hitting the ground.