SOLUTION: 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

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): You can put this solution on YOUR website!
Ankor, many thanks for solve this problem. Have stuck with my project assignment. Since this one isn't probably going to make it, maybe you could do this project again with some changes.
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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