Question

HELP ME PLEASE!!! A ball is thrown in the air from a platform that is 112 feet above ground level with an initial vertical velocity of 32 feet per second. The height of the ball, in feet, can be represented by the function shown where t is the time, in seconds, since the ball was thrown.


h(t)=−16t2+32t+112

Which of the following equations shows the function rewritten in the form that would be best used to identify the maximum height of the ball?


Question 16 options:


h(t)=−16(t−2)2+112


h(t)=−16(t−1)2+80


h(t)=−16(t−1)2+96


h(t)=−16(t−1)2+128

Answer 1

The ball thrown upwards follows a parabolic path

The equation that shows the function rewritten in the form that would be best used to identify the maximum height of the ball is $h(t)=-16(t-1)^2+128$

How to determine the equivalent equation

The equation is given as:

$h(t)=-16t^2+32t+112$

Factor out -16

$h(t)=-16(t^2-2t)+112$

Express the bracket as a perfect square expression

$h(t)=-16(t^2-2t + 1 - 1)+112$

Factor out -4

$h(t)=-16(t^2-2t + 1)+112 + 16 * 1$

$h(t)=-16(t^2-2t + 1)+128$

Express as a perfect square

$h(t)=-16(t-1)^2+128$

Hence, the equivalent expression is $h(t)=-16(t-1)^2+128$

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