The flight of a baseball that was hit when it was 4 feet off the ground is modeled by the function h=−16t2+75t+4
, where h is the height of the baseball, in feet, after t seconds.

How long does it take the baseball to reach its maximum height? Round to the nearest tenth.

__________ seconds

The function modeling the baseball's height is:

\[
h = -16t^2 + 75t + 4
\]

This is a quadratic function in the form \( h = at^2 + bt + c \), where:
- \( a = -16 \)
- \( b = 75 \)

To find the time it takes for the baseball to reach its maximum height, we use the formula for the vertex of a parabola, given by:

\[
t = -\frac{b}{2a}
\]

Substitute \( a = -16 \) and \( b = 75 \):

\[
t = -\frac{75}{2 \times -16} = \frac{75}{32} \approx 2.3
\]

So, the time it takes for the baseball to reach its maximum height is approximately **2.3 seconds**.

Would you like a breakdown of the steps or further questions on this topic?

Here are five related questions that might interest you:
1. What is the maximum height of the baseball?
2. When does the baseball hit the ground?
3. How would the maximum height change if the initial velocity was different?
4. What effect would air resistance have on the flight of the baseball?
5. How does the initial height affect the time to reach maximum height?

**Tip:** The vertex formula \( t = -\frac{b}{2a} \) works for any quadratic function to find the maximum or minimum point, depending on the direction of the parabola.

How long does it take the baseball to reach its maximum height? Round to the nearest tenth.

Learn how to determine the time it takes for a baseball to reach its maximum height using the quadratic function h = -16t^2 + 75t + 4. This lesson covers the vertex formula application, ideal for students in Grades 8-10.

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