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We are given a quadratic equation that models the path of a football:

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

Here, \( h(x) \) represents the height of the football, and \( x \) represents the horizontal distance in yards. The goal is to determine how far the ball will have traveled when it hits the ground, which means solving for \( x \) when \( h(x) = 0 \).

The equation to solve is:

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

Now, let's solve this step by step.

1. Factor the equation:

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

2. Set each factor equal to zero:

\[
x = 0 \quad \text{or} \quad x - 61 = 0
\]

Solving for \( x \) in the second equation:

\[
x = 61
\]

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

Would you like further details on this process or have any questions?

Here are five related questions to deepen your understanding:

1. What does each part of the quadratic function represent in a real-world scenario like this one?
2. How would the function change if the football were kicked higher or lower?
3. Can you graph the path of the football using the given quadratic equation?
4. What does the value \( x = 0 \) represent in this context?
5. How would air resistance affect this type of quadratic model?

**Tip:** Quadratic functions that describe the motion of projectiles often have a maximum point, representing the highest point the object reaches during its flight.

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.

Solve the quadratic equation h(x) = -1/30 * x * (x - 61) to determine how far a football will travel before hitting the ground. This step-by-step solution covers concepts in quadratic equations and factoring. Suitable for students in Grades 9-10.

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