Question

the height of a ball is modeled by the function (h(t) = -4t^2 + 8t), where the height, (h(t)), is measured in feet and (t) is the time in seconds. what is the maximum height of the ball?

1 foot
2 feet
4 feet
8 feet

Explanation:

Identify the quadratic function parameters

$$ h(t) = -4t^2 + 8t \implies a = -4, \quad b = 8, \quad c = 0 $$

Calculate the time at maximum height

$$ t_v = -\frac{b}{2a} = -\frac{8}{2(-4)} = 1\text{ second} $$

Evaluate the maximum height

$$ h(1) = -4(1)^2 + 8(1) = -4 + 8 = 4\text{ feet} $$

Answer:

• 1 foot
• 2 feet
• 4 feet (Correct answer)
• 8 feet