Question 329756: A rock is launched from a cannon its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.
After 1 second, the rock is 186 feet in the air after 2 seconds, it is 344 in the air.
Find the height, in feet,of the rock after 8 seconds in the air.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rock is launched from a cannon its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.
After 1 second, the rock is 186 feet in the air; after 2 seconds, it is 344 in the air.
Find the height, in feet,of the rock after 8 seconds in the air.;
:
Using the form: ax^2 + bx + c = y
y = h(x), c = 0
:
x=1; y=186
a(1^2) + 1b = 186
a + b = 186
:
x=2; y=344
a(2^2) + 2b = 344
4a + 2b = 344
:
Multiply the 1st equation by 2, subtract from the 2nd equation
4a + 2b = 344
2a + 2b = 372
--------------Subtraction eliminates b, find a
2a = -28
a = -14
:
Find b using: a + b = 186
-14 + b = 186
b = 186 + 14
b = 200
:
The equation: h(x) = -14x^2 + 200x
:
"Find the height, in feet,of the rock after 8 seconds in the air.;
x=8
h(8) = -14(8^2) + 200(8)
h(8) = -14(64) + 1600
h(8) = -896 + 1600
h(8) = 704 ft after 8 sec
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