Answer:
20 m
Step-by-step explanation:
The maximum height is given by the vertex form of the equation, that is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
h(t) = - 5t² + 20t ← factor out - 5 from each term
= - 5(t² - 4t)
Using the method of completing the square
add/subtract ( half the coefficient of the t- term)² to t² - 4t
h(t) = - 5(t² + 2(- 2)t + 4 - 4 )
= - 5(t - 2)² + 20 ← in vertex form
with vertex = (2, 20 )
The maximum height is at the value of k = 20
That is the maximum height is 20 m
