Question 749246: Have a project with Angry Birds where you have to find the equation of a parabola for the bird's flight path in various situations. I have to pick a point at the origin and a pint on the x axis for the pig to be placed and find the flight path (equation). How would i do this? I chose for points:
Bird placed at (0,0)
Pig placed at (5,0)
I dont understand what to do after this please help.
Found 3 solutions by ankor@dixie-net.com, ValerieDavis, Alan3354:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Have a project with Angry Birds where you have to find the equation of a parabola for the bird's flight path in various situations.
I have to pick a point at the origin and a point on the x axis for the pig to be placed and find the flight path (equation).
How would i do this? I chose for points:
Bird placed at (0,0)
Pig placed at (5,0)
:
We need another point, 0,0 is of no use, lets choose 3,4 as a point
:
Using the form ax^2 + bx + c = y
We are using origin so we can ignore c, just find a and b
:
Write an equation for each point, find a and b
:
Point: 5,0
25a + 5b = 0
and
Point 3,4
9a + 3b = 4
:
Multiply the 1st equation by 3, the 2nd equation by 5
75a + 15b = 0
45a + 15b = 20
------------------subtraction eliminates b, find a
30a = -20
a = -20/30
a = -.67
Use the 1st equation to find b
25(-.67) + 5b = 0
-16.67 + 5b = =
5b = 16.67
b = 16.67/5
b = 3.33
:
The equation: y = -.67x^2 + 3.33x
looks like this
Answer by ValerieDavis(6)  (Show Source):
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Have a project with Angry Birds where you have to find the equation of a parabola for the bird's flight path in various situations. I have to pick a point at the origin and a pint on the x axis for the pig to be placed and find the flight path (equation). How would i do this? I chose for points:
Bird placed at (0,0)
Pig placed at (5,0)
I dont understand what to do after this please help.
--------------------
The points are on the x-axis, so the vertex of the parabola is on the line x = 2.5, thru the midpoint.
----
There are an infinite # of parabolas that will fit, only the y value of the vertex varies.
---
the simplest method is to start with a parabola with its vertex on the y-axis, then shift it to the right 2.5 units.
y = -5x^2 + will work.
then the shift --> y = -5(x-2.5)^2 + 6.25
===============
You can use the 3 points (0,0), (5,0) and (2.5,y) also.
Pick any value for y > 0 and find a parabola that fits.
eg (2.5,5)
---
y = ax^2 + bx + c
0 = c
----
5 = a*6.25 + 5*2.5 = 6.25a + 12.5
a = -7.5/6.25 = -1.2
b = 6
--> y = -1.2x^2 + 6x
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