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 time \( x \) wasn't provided in your message. To determine the maximum height reached by the rocket, I need the specific equation that models its motion. Typically, rocket height as a function of time can be modeled by a quadratic equation of the form: \[ y = ax^2 + bx + c \] If you can provide the exact equation, I'd be happy to help you find the maximum height to the nearest tenth of a foot! **Example:** If the height equation were: \[ y = -16x^2 + 160x + 20 \] Here's how you'd find the maximum height: 1. **Identify the coefficients:** - \( a = -16 \) - \( b = 160 \) 2. **Find the time at which the maximum height occurs:** The vertex of a parabola \( y = ax^2 + bx + c \) occurs at \( x = -\frac{b}{2a} \). \[ x = -\frac{160}{2(-16)} = \frac{160}{32} = 5 \text{ seconds} \] 3. **Calculate the maximum height:** Substitute \( x = 5 \) back into the equation: \[ y = -16(5)^2 + 160(5) + 20 = -400 + 800 + 20 = 420 \text{ feet} \] So, the maximum height reached is **420.0 feet**. Please provide the specific equation for a precise answer!