Question

the height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function \\(f(t) = -16t^2 + 48t\\), where \\(t\\) is the time in seconds since the rocket was shot and \\(f(t)\\) is the rockets height in feet. what is the maximum height the rocket reaches?

16 ft
36 ft
48 ft
144 ft

Explanation:

Find the time at the vertex

$$ t = -\frac{b}{2a} = -\frac{48}{2(-16)} = 1.5\text{ s} $$

Calculate the maximum height

$$ f(1.5) = -16(1.5)^2 + 48(1.5) = -16(2.25) + 72 = -36 + 72 = 36\text{ ft} $$

Answer:

• 16 ft
• 36 ft (Correct answer)
• 48 ft
• 144 ft