SOLUTION: Please help me with this function notation word problem! "Use function notation to rewrite the following phrases below. A ball is thrown straight up with a certain speed, then it

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Question 1185467: Please help me with this function notation word problem!
"Use function notation to rewrite the following phrases below.
A ball is thrown straight up with a certain speed, then its height above the ground (measured in meters) after t seconds is given by the following equation:
h(t) = −4.9t2+30t
1. The height of the ball 1 second after being thrown
2. The height of the ball 2 seconds after being thrown
3. The height of the ball t seconds after being thrown
4. The change in height of the ball between 1 and 2 seconds
5. The change in height of the ball between 1.5 and 2.5 seconds
6. The change in height of the ball between a and b seconds"
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.