Can You Give The Answer? The Function Gives The Height, Batted Baseball As A Function Of The Time, Since The Ball Was Hit. H= -6(t - 2.5)² + 38.5

We can see that this is an inverted parabola because it's second order (t²) and negative

begin by expanding the binomial:
H = -6 (t² - 5t + 6.25) + 38.5

multiply through by NEGATIVE 6:
H = -6t² + 30t - 37.5 + 38.5

add in the 38.5:
H = -6t² + 30t + 1

set t=0 and solve for H to find out when it started (time is measured from the start of its trajectory)

maximum height requires a derivative set to zero and solved for a local maxima
H` = -12t + 30 = 0  (this is the slope of a tangent line to the balls tragectory, which is zero at the top of the parabola)

set H to zero and solve for t for when it hits the ground (you'll get two answers, one when it started, one when it landed.  never mind that this ball doesn't bounce!)

also set t=1 (sec) for part D


Show your work below and I'll check it
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Bant I believe this is a more easily understood explanation:
 
 
In order to solve this problem I will use differential calculus as follows
 
 
h=-6(t-2.5)2+30t+1=-6t2+30t+1
 
h'(t)=-12t+30
 
a.) for the max height of the ball
 
The vertex of an inverted parabola would be calculated as follows:
 
h'(t)=-12t+30=0 solve for t= 2.5 therefore 113.5ft max height
 
b.) 5 seconds to hit the ground
 
c.) The height of the ball 1 sec after hit
 
h=-6t²+30t+1 therefore h(1)= 25 ft.
 
 

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