SOLUTION: A gound base missile is launched from the origin (0,0), it reaches a maximum height of 10km and lands 200km away at the point (200,0) determine the quadratic equation. The missiles

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Question 447407: A gound base missile is launched from the origin (0,0), it reaches a maximum height of 10km and lands 200km away at the point (200,0) determine the quadratic equation. The missiles flight path is a parabola.
Answer by ankor@dixie-net.com(22740) (Show Source):
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A gound base missile is launched from the origin (0,0),
it reaches a maximum height of 10km and lands 200km away at the point (200,0)
determine the quadratic equation. The missiles flight path is a parabola.
:
The max height is halfway between launch and impact point: 100 km
:
Two ordered pairs: 100, 10 and 200, 0
Using the form ax^2 + bx + c = y; c = 0 here so we have:
100, 10
100^2*a + 100b = 10
10000a + 100b = 10
and
200, 0
200^2*a + 200b = 0
40000a + 200b = 0
multiply the 1st equation by 2, subtract from the above equation
40000a + 200b = 0
20000a + 200b = 20
---------------------subtraction eliminates b, find a
20000a = -20
a =
a = -.001
:
Find b using the 1st equation
10000(-.001) + 100b = 10
-10 + 100b = 10
100b = 10 + 10
100b = 20
b =
b = .2
:
The equation: y = -.001x^2 + .2x
:
looks like this;