Question 1195808: A toy rocket is fired off the ground at a target 20 feet away. It is designed to reach a maximum height of 40 feet as it heads toward its target on a parabolic path. Find the equation that represents the height off the ground versus the distance travelled for this rocket
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A toy rocket is fired off the ground at a target 20 feet away. It is designed to reach a maximum height of 40 feet as it heads toward its target on a parabolic path. Find the equation that represents the height off the ground versus the distance travelled for this rocket
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Put the apogee above the Origin.
3 points on the parabola are
A(-10,0), B(0,40) and C(10,0)
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y = ax^2 + bx + c is a parabola
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Point A:
0 = a*(-10)^2 + b*-10 + c = 0
100a - 10b + c = 0
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Point B:
a*0 + b*0 + c = 40 ---> c = 40
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Point C:
a*(10)^2 + b*10 + c = 0
100a + 10b + c = 0
100a - 10b + c = 0 --- Point A
---------------------------------------- Subtract
20b = 0
b = 0
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100a - 10b + c = 0 --- Point A
100a + c = 0
100a + 40 = c
a = -0.4
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y = -0.4x^2 + 40 is the equation WITH the center at the Origin.
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