Question 77495: I am having trouble finding the x-intercepts for the following situation.
The quarterback is standing on the opponents' 40-yard line. He throws a pass toward their goal line. The ball is 2 meters above the ground when the quarterback lets go. It follows a parabolic path, reaching its highest point, 14 meters above the ground, as it crosses the 20-yard line.
Can you Please help???? Thank you in advance.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I am having trouble finding the x-intercepts for the following situation.
The quarterback is standing on the opponents' 40-yard line. He throws a pass toward their goal line. The ball is 2 meters above the ground when the quarterback lets go. It follows a parabolic path, reaching its highest point, 14 meters above the ground, as it crosses the 20-yard line.
:
How about this?
let the x = the yards from the point of throwing of the pass
The y = height of the football.
:
When the pass was thrown, x = 0 and y = 2; (also c = 2 in ax^2 + bx + c form)
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At the highest point. x = 20 and y = 14
:
Since it is a parabola:
From y = 2 meters and the highest point is at 20 yds,
then at 40 yds, y will also = 2: so we have: x = 40; y = 2
:
Find a and b in the equation ax^2 + bx + c:
:
x = 20, y = 14
400a + 20b + 2 = 14
400a + 20b = 12; subtracted 2 from both sides:
:
x = 40, y = 2
1600a + 40b + 2 = 2
1600a + 40b = 0; subtracted 2 from both sides
:
Use the elimination method
Multiply the 1st equation by 4 and subtract from the 2nd equation to find b:
1600a + 40b = 0
1600a + 80b = 48
-------------------subtract
0 - 40b = -48
b = -48/-40
b = +1.2
:
Find a in 400a + 20b = 12, substitute 1.2 for b
400a + 20(1.2) = 12
400a + 24 = 12
400a = -12
400a = -12/400
a = -.03
:
Our equation would be: -.03x^2 + 1.2x + 2 = 0
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A graph would look like this:
:
The x intercept would be when it hit the ground in the end zone, (assuming no one caught it)
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Find the x intercept using the quadratic formula a = -.03; b = 1.2; c = 2
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You should get a positive solution of about 41.6 yds, or 1.6 yds into the end zone
:
Did this make sense to you? Thanks for an interesting problem.
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