To find the height of the balloon at $t = 2$ seconds, substitute $t = 2$ into the function $h(t) = 5t^2 - 3t + 10$:

$h(2) = 5(2)^2 - 3(2) + 10$

Step 1: Evaluate each term

• $5(2)^2 = 5 \times 4 = 20$
• $-3(2) = -6$
• Constant term: $+10$

Step 2: Add the terms

$h(2) = 20 - 6 + 10 = 24$

Final Answer:

The height of the balloon at $t = 2$ seconds is 24 meters.

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Interpretation in context:

At $t = 2$ seconds, the weather balloon has risen to a height of 24 meters above the ground.

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Do you want details on solving similar quadratic function problems?
Here are 5 questions to deepen your understanding:

1. What is the balloon's initial height (at $t = 0$)?
2. At what time does the balloon reach its minimum height?
3. What does the coefficient of $t^2$ (i.e., 5) tell us about the balloon's motion?
4. How does changing the $t$-coefficient ($-3$) affect the motion?
5. Can we use this function to determine when the balloon will reach a specific height?

Tip: Always substitute carefully into the formula, keeping track of parentheses to avoid sign errors.