After t seconds a ball tossed In the air from the ground level reaches a height and of h feet given by the function h(t)=144t-16t^2 1) When will the ball reach the maximum height?

Check the explantion

Step-by-step explanation:

H(t) represent the height of the ball after t seconds.

1)

In order to figure the maximum height of the ball we must minupulate this equation into a form where we can easily find the maximum height.

We can also see this parabola will be downward concaved because it has a negative coefficent for the t^2 term.

a) Let's Manipulate!

Vertex form is a form where we can easily tell the maximum and minimum points. To get in into Vertex form we just need to complete the sqaure.

Lets reanrage the terms

h(t)= -16t^2+144t

Undo the distrubitive propety

h(t)= -16(t^2-9t+20.25)+324

Add and subtract 324.

h(t) = -16(t-4.5)^2+324

COmplete the square.

b) Almost done!

We can now see that the stuff with the brackets is always positive/zero because any real number sqaured is a positive/zero. But than we multiply the positive stuff by a negative number (-16) so its now all negative.

The only exception is when its zero.

And off course if we add 324 to zero its always going to be greater than 324 + a negative number. To get the first term to be zero we can have t = 4.5.

c) Proove it!

h(4.5) = -16(4.5-4.5)^2+324

=324

d) Double Check by graphing!

(Its a attach screenshote by the way)

e)

The ball will reach its maximum height after 4.5 seconds.

Hoped this helped!,

JoeLouis2

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step-by-step explanation: