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Using the equation representing the height of the firework (h = 16t2 + v0t + h0), algebraically determine the extreme value of f(t) by completing the square and finding the vertex. Interpret what the value represents in this situation.

for y = ax^2 + bx + c, the x of the vertex is b/(2a)
so for h = 16t2 + v0t + h0 , the t of the vertex is v0/32 = v0/32
h = 16(v0^2/1024) + (v0)^2 + h0
= v0/32 + v0^2 + h0
vertex is (v0/32 , v0/32 + v0^2 + h0)
check my algebra, I did not write it out first.posted by Reiny

for y = ax^2 + bx + c, the x of the vertex is b/(2a)
so for h = 16t2 + v0t + h0 , the t of the vertex is v0/32 = v0/32
h = 16(v0^2/1024) + (v0)^2 + h0
= v0/32 + v0^2 + h0
vertex is (v0/32 , v0/32 + v0^2 + h0)
check my algebra, I did not write it out first.posted by Reiny

Recall that for ax^2+bx+c the vertex lies at (b/2a, (4acb^2)/4a)
Now just plug in your coefficientsposted by Steve
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