It seems like the equation you're trying to write has some formatting issues. Let's correct and break it down. Based on what you wrote, I assume you intended to write:

\[
h(t) = -16t^2 + 343t + 12
\]

This appears to be a quadratic equation in \( t \), likely representing the height \( h(t) \) of an object (such as a projectile) over time, where:
- The term \( -16t^2 \) accounts for the acceleration due to gravity (assuming units of feet and seconds),
- The term \( 343t \) could represent the initial velocity of the object,
- The constant \( 12 \) is the initial height.

Let me know if this is correct, and if you'd like, I can help you analyze this equation further (e.g., finding the time when the object reaches maximum height, the time it hits the ground, etc.).

Would you like me to proceed with solving or analyzing this equation?

### Follow-up Questions:
1. Do you want to find the maximum height of the object?
2. Are you interested in determining when the object hits the ground?
3. Would you like to know how to complete the square for this equation?
4. Do you need help with plotting the graph of this equation?
5. Would you like to learn how to factor or solve this quadratic equation?

### Tip:
In projectile motion, the coefficient of \( t^2 \) (here, -16) represents half the acceleration due to gravity, so in feet per second, the acceleration is \( -32 \, \text{ft/s}^2 \).

Learn how to solve the quadratic equation h = -16t^2 + 343t + 12 in the context of projectile motion. This problem explores key algebraic concepts like quadratic equations and involves solving for maximum height and the time the object hits the ground. Suitable for high school students in Grades 9-12.

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