Question 177929
By inspecting:
y=-3x^2+18x+1
We see that the first coefficient is -3, this means it's a parabola in the shape of an "upside down U".  This means, if we find the "vertex" of the parabola, it will be at the peak of the parabola.
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The idea is to "complete the square" to get it into the "standard vertex" form:
y= a(x-h)^2+k 
where (h,k) is the maximum.
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y=-3x^2+18x+1
y=(-3x^2+18x)+1
y=-3(x^2-6x)+1
y=-3(x^2-6x+9)+1+27
y=-3(x-3)(x-3)+28
y=-3(x-3)^2+28
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Therefore,
(h,k)= (3,28)
This says, that at 3 seconds the ball is at the peak of 28 meters.