Question 687613
h = 4.52t^2 + .41t + 5.92
Factor 4.52 from the 1st two terms.
Then complete the square on the right side
Be sure you maintain the equality by subtracting what you added.
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h  = 4.52(t^2 + (0.41/4.52)t + (0.41/9.04)^2)+ 5.92 - 4.52(0.41/9.04)^2
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h = 4.52(t+(0.41/9.04))^2 + 5.91
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Vertex is (-0.41/9.04 , 5.91), so the minumum height is 5.91
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Note: That is what you asked for, but I don't that is what
you want.  
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Cheers,
Stan H.