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The given function is \( h(x) = -x^2 + 6x \), and we are asked to find \( h(5) \).

To do this, substitute \( x = 5 \) into the equation:

\[
h(5) = -(5)^2 + 6(5)
\]
\[
h(5) = -25 + 30
\]
\[
h(5) = 5
\]

Thus, the value of \( h(5) \) is \( 5 \).

Would you like more details on this solution? Here are 5 related questions to explore:

1. How do you find the maximum height of the water in the fountain modeled by this equation?
2. What is the vertex of the parabola described by \( h(x) = -x^2 + 6x \)?
3. How can we determine when the water in the fountain hits the ground?
4. How do you calculate the horizontal distance at which the water reaches the maximum height?
5. How does the coefficient of \( x^2 \) affect the shape of the parabolic path?

**Tip:** The highest or lowest point on a parabola can be found using the vertex formula \( x = -\frac{b}{2a} \) for a quadratic equation \( ax^2 + bx + c \).

The function h(x) = -x^2 + 6x models the path of water in a fountain (in meters). The function represents the vertical distance, h, as a function of the horizontal distance, x. What is the value of h(5)?

In this problem, we solve the quadratic function h(x) = -x^2 + 6x by substituting x = 5. This question explores concepts of quadratic functions and substitution, suitable for students in Grades 8-10.

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