SOLUTION: A baseball is hit and follows a parabolic path described by the function y=-3x^2+18x+1, where x represents the time in seconds after the ball is hit and y represents the ball's hei

Question 177929: A baseball is hit and follows a parabolic path described by the function y=-3x^2+18x+1, where x represents the time in seconds after the ball is hit and y represents the ball's height in meters from the ground. Algebraically determine the maximum height and the time at which the ball reaches its maximum height.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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.
.
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.
.
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
.
Therefore,
(h,k)= (3,28)
This says, that at 3 seconds the ball is at the peak of 28 meters.

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