To find the initial height of the ball when it was kicked, we need to evaluate the height function \( h(T) \) at \( T = 0 \).

The height function is given by:
\[ h(T) = \frac{2}{7} (T + 3)(7 - T) \]

Substitute \( T = 0 \) into the equation:
\[ h(0) = \frac{2}{7} (0 + 3)(7 - 0) \]

Simplify the expression:
\[ h(0) = \frac{2}{7} \cdot 3 \cdot 7 \]

\[ h(0) = \frac{2}{7} \cdot 21 \]

\[ h(0) = 6 \]

Therefore, the initial height of the ball when it was kicked is 6 units.

Would you like more details on this solution or have any other questions?

Here are 5 more questions you might ask:

1. How do you find the maximum height the ball reaches?
2. Can you derive the time at which the ball reaches its maximum height?
3. What is the significance of the coefficients in the height equation?
4. How does the shape of the trajectory change with different coefficients?
5. What is the time interval during which the ball is above the pier?

**Tip:** When evaluating a function at a specific point, carefully substitute the value into the equation and simplify step by step to avoid errors.

Learn how to calculate the initial height of a ball using a quadratic function. Step-by-step solution provided for evaluating the height function at T = 0. Suitable for high school students studying functions and quadratic equations.

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