1. **State the problem:** We are given the height of a rocket as a function of time: $$y = -16x^2 + 235x + 67$$ where $y$ is the height in feet and $x$ is the time in seconds. We need to find the maximum height reached by the rocket. 2. **Identify the type of function:** This is a quadratic function in the form $$y = ax^2 + bx + c$$ with $a = -16$, $b = 235$, and $c = 67$. Since $a < 0$, the parabola opens downward, so the vertex represents the maximum point. 3. **Formula for the vertex:** The $x$-coordinate of the vertex is given by $$x = -\frac{b}{2a}$$ 4. **Calculate the time at maximum height:** $$x = -\frac{235}{2 \times -16} = -\frac{235}{-32} = \frac{235}{32}$$ 5. **Calculate the maximum height by substituting $x$ back into the equation:** $$y = -16\left(\frac{235}{32}\right)^2 + 235\left(\frac{235}{32}\right) + 67$$ 6. **Simplify step-by-step:** $$y = -16 \times \frac{235^2}{32^2} + 235 \times \frac{235}{32} + 67$$ $$y = -16 \times \frac{55225}{1024} + \frac{235^2}{32} + 67$$ $$y = -\frac{16 \times 55225}{1024} + \frac{55225}{32} + 67$$ $$y = -\frac{883600}{1024} + \frac{55225}{32} + 67$$ 7. **Simplify fractions:** $$-\frac{883600}{1024} = -862.5$$ $$\frac{55225}{32} = 1725.78125$$ 8. **Add all terms:** $$y = -862.5 + 1725.78125 + 67 = 930.28125$$ 9. **Round to the nearest tenth:** $$\boxed{930.3}$$ feet is the maximum height reached by the rocket.