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The quadratic function given is:

\[
h(x) = 3 - 32x - 32x^2
\]

This is a quadratic equation in the standard form \( h(x) = ax^2 + bx + c \), where:

- \( a = -32 \) (the coefficient of \(x^2\)),
- \( b = -32 \) (the coefficient of \(x\)),
- \( c = 3 \) (the constant term).

### Key Information:
- The function opens downward because the coefficient of \(x^2\) is negative (\(a = -32\)).
- The vertex represents the maximum point of the function since it opens downward.

To analyze this further, we can:
1. Find the vertex of the parabola.
2. Determine the axis of symmetry.
3. Calculate the maximum value of \(h(x)\).
4. Find the x-intercepts or roots (if they exist).
5. Discuss the behavior of the function at large values of \(x\).

Would you like me to go through one of these steps or all of them? Let me know if you need any specific details!

Here are 5 related questions to expand your understanding:
1. How do you find the vertex of a quadratic function?
2. How can you determine the axis of symmetry of a quadratic equation?
3. What is the significance of the sign of the \(a\)-value in a quadratic equation?
4. How do you find the x-intercepts (roots) of this function?
5. Can you express this function in vertex form?

**Tip:** In a quadratic function, the vertex form \(h(x) = a(x - h)^2 + k\) provides useful insight into the function's maximum or minimum value and the vertex location.

A quadratic function h(x) = 3 - 32x - 32x^2 is given. Analyze the function's properties, including its vertex, axis of symmetry, and maximum value.

Explore the properties of the quadratic function h(x) = 3 - 32x - 32x^2, including its vertex, axis of symmetry, and maximum value. This problem is ideal for students in Grades 9-11, focusing on algebraic concepts and quadratic functions.

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