Final answer:
The maximum height reached by the bottle rocket is 9.8 feet, which is found by determining the vertex of the quadratic equation representing the rocket's height over time.
Step-by-step explanation:
The equation given for the height of a bottle rocket is a quadratic equation of the form h = -5t^2 + 14t + 3. The maximum height of the bottle rocket can be found by analyzing the vertex of the parabola represented by this equation. The time at which the maximum height is reached is found using the formula t = -b/(2a), applied to the coefficients of the equation.
To find the maximum height, we first calculate the time at which it occurs: t = -14/(2×(-5)) = 14/10 = 1.4 seconds. Then, we plug this time back into the original equation to get the maximum height: h = -5(1.4)^2 + 14(1.4) + 3, which calculates to h = 9.8 feet.
Therefore, the correct answer is D. 9.8 feet.