A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after aunch, x in seconds, by the given equation. Using this equation, find the maximum height eached by the rocket, to the nearest tenth of a foot.

It looks like the equation relating the rocket's height \( y \) to the time \( x \) after launch wasn't provided. To determine the maximum height reached by the rocket, the specific form of the equation is essential. Typically, such equations are quadratic (of the form \( y = ax^2 + bx + c \)), where the maximum height can be found by analyzing the vertex of the parabola. **Here's what you can do:** 1. **Provide the Equation:** If you have the specific equation, please share it so I can help you calculate the maximum height accurately. 2. **General Approach (If the Equation is Quadratic):** - **Standard Form:** Assume \( y = ax^2 + bx + c \). - **Vertex Formula:** The time at which the maximum height occurs is \( x = -\frac{b}{2a} \). - **Maximum Height:** Substitute this \( x \) value back into the equation to find \( y \). **Example:** Suppose the height equation is \( y = -16x^2 + 64x + 80 \). 1. **Find the Time at Maximum Height:** \[ x = -\frac{b}{2a} = -\frac{64}{2(-16)} = 2 \text{ seconds} \] 2. **Calculate the Maximum Height:** \[ y = -16(2)^2 + 64(2) + 80 = -64 + 128 + 80 = 144 \text{ feet} \] So, the rocket reaches a maximum height of **144.0 feet**. Please provide the specific equation if you need a precise calculation!