Abaseball is thrown upward and its height after t seconds can be described by formula h(t)=−16t2+50t+5. find the maximum height the ball will reach.

h(t) = -16t² + 50t + 5

The maximum height is the y vertex of this parabola.

Vertex = (-b/2a, -Δ/4a)

The y vertex is -Δ/4a

So,

The maxium height is -Δ/4a

Δ = b² - 4.a.c

Δ = 50² - 4.(-16).5

Δ = 2500 + 320

Δ = 2820

H = -2820/4.(-16)

H = -2820/-64

H = 2820/64

H = 44.0625

So, the maxium height the ball will reach is 44.0625

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