Question 1185467
the function is:


h(t) = -4.9 * t^2 + 30*t


t^2 means t raised to the second power.


answers to your questions are shown below:


1. The height of the ball 1 second after being thrown


h(1) = -4.9 * 1^2 + 30*1 = 25.1 meters


2. The height of the ball 2 seconds after being thrown


h(2) = -4.9 * 2^2 + 30 * 2 = 40.5 meters



3. The height of the ball t seconds after being thrown


h(t) = -4.9 * t^2 + 30 * t



4. The change in height of the ball between 1 and 2 seconds


h(2) - h(1) = -4.9 * 2^2 + 30 * 2 - (-4.9 * 1^2 + 30 * 1) = 15.3 meters


5. The change in height of the ball between 1.5 and 2.5 seconds


h(2.5) - h(1.5) = -4.9 * 2.5^2 + 30 * 2.5 - (-4.9 * 1.5^2 + 30 * 1.5) = 10.4 meters


6. The change in height of the ball between a and b seconds"


h(b) - h(a) = -4.9 * b^2 + 30 * b - (-4.9 * a^2 + 30 * a) equals:
-4.9 * b^2 + 30 * b + 4.9 * a^2 - 30 * a  ***** 1
you can reorder the terms in descending order of degree as shown below:
-4.9 * b^2 + 4.9 * a^2 + 30 * b - 30 * a.  ***** 1
you can factor the terms as shown below:
factor out the -4.9 and factor out the 30 to get:
-4.9 * (b^2 - a^2) + 30 * (b - a) ***** 1


***** 1
you can use either version and you should be ok.


the factored version should be equivalent to the unfactored version.
you can check to see if this is good by using one of the previous problems.
for example: 
h(2.5) - h(1.5) becomes:
4.9 * (-(2.5^2 + 1.5^2) + 30 * (2.5 - 1.5) which becomes:
-4.9 * 4 + 30 which iw equal to 10.4.


this confirms the factoring was good.
if you try to do this yourself, be careful of the minus signs.
they can mess up your calculations.
i had to do it a couple of time before i got it right.