Madison launches a toy rocket from a platform. The height of the rocket in feet is given by h, equals, minus, 16, t, squared, plus, 80, t, plus, 44*h*=−16*t*2+80*t*+44 where t*t* represents the time in seconds after launch. What is the rocket’s initial height?

The height of the rocket is given by the equation:

\[
h(t) = -16t^2 + 80t + 44
\]

To find the initial height of the rocket, we need to determine the height at time \( t = 0 \). By substituting \( t = 0 \) into the equation:

\[
h(0) = -16(0)^2 + 80(0) + 44 = 44
\]

Thus, the initial height of the rocket is **44 feet**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the maximum height reached by the rocket?
2. At what time does the rocket reach its maximum height?
3. How long does it take for the rocket to hit the ground?
4. What is the height of the rocket at \( t = 2 \) seconds?
5. How can the equation be used to determine the velocity of the rocket at any time?

**Tip:** The initial height is always the constant term in a quadratic height equation like this one.

Madison launches a toy rocket from a platform. The height of the rocket in feet is given by h = -16t^2 + 80t + 44, where t represents the time in seconds after launch. What is the rocket’s initial height?

Find the initial height of a rocket using the quadratic equation h = -16t^2 + 80t + 44. This problem covers key algebra concepts and kinematics, including determining the height at t = 0 and analyzing projectile motion. Suitable for students in Grades 8-10.

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