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Angry Birds Quadratic Project
4,053
Quadratics Project
Makenna Larson
Version 1
Black Bird flew the highest: 32 yards
Red Bird flew the longest: 28 yards
Yellow Bird hit Mustache Pig.
Black Bird hit King Pig.
Red Bird
Red Bird starts his from point (10,0). His flight path reaches a maximum of 18 yards and lands at point (38,0).
How I Got Equation
18=a(x-10)(x-38)
(24,18)
18=a(24-10)(24-38)
18=a(14)(-14)
18=a(-196)
-196
Given: (10,0), (38,0)
Max. Height:18
Equation: y=-9/98(x-10)(x-38)
Vertex: (24,18)
Axis of Symmetry: x=24
Zeros: (10,0), (38,0)
Flight Distance: 28 yards
Max. Height: 18 yards
Domain: [10,38]
Range: [0,18]
Areas of Increase: (10,24)
Areas of Decrease: (24,38)
(38,0)
(10,0)
.
The starting point and the end points were given. To find the distance traveled I took 38-10 and I got 28. The maximum height was also given (which is 18).
Blue Bird
Yellow Bird
Blue Bird's flight is represented by the graph below...
Yellow Bird's flight path can be modeled by the quadratic equation.
y=-x^2+14x-24
(13,12)
.
(7,25)
How I Found Zeroes
y=-(x^2-14x+24)
0=-(x-12)(x-2)
x=2,12
How I Found
Axis Of Symmetry
x=-b/2a
x=-14/2(-1)
x=7
.
(26,0)
(0,0)
Given: graph
Equation: y=-12/169(x-0)(x-26)
Vertex: (13,12)
Axis of Symmetry: x=13
Zeros: (0,0), (26,0)
Flight Distance: 26 yards
Max. Height: 12 yards
Domain: [0,26]
Range: [0,13]
Areas of Increase: (0,13)
Areas of Decrease: (13,26)
Given: equation
Equation: y=-x^2+14x-24
Vertex: (7,25)
Axis of Symmetry: x=7
Zeros: (2,0), (12,0)
Flight Distance: 10 yards
Max. Height: 25 yards
Domain: [2,12]
Range: [0,7]
Areas of Increase: (2,7)
Areas of Decrease: (7,12)
Since I was given the equation, I plugged the equation into Desmos to make a graph. I used the graph to find the maximum height.
I had to estimate what the maximum height because it was hard to tell what the maximum height was by the graph. My answers could somewhat vary from the actual answer because of this. To find the flight distance I subtracted the two zeros. To find the axis of symmetry I divided the flight distance by two to get 13.
(2,0)
(12,0)
.
The table below contains partial data points of Black Bird's trajectory.
Black Bird
8 9 10 11 12 13 14 15 16 17 18
0 7.5 14 19.5 24 27.5 30 31.5 32 31.5
(16,32)
How I Found
the Equation
32=a(16-8)(16-24)
32=a(8)(-8)
32=a(-64)
-64
Given: table
Equation: y=-1/2(x-8)(x-24)
Vertex: (16,32)
Axis of Symmetry: x=16
Zeros: (8,0), (24,0)
Flight Distance: 16 yards
Max. Height: 32 yards
Domain: [8,24]
Range: [0,32]
Areas of Increase: (8,16)
Areas of Decrease: (16,24)
1/2=a
y=1/2(x-8)(x-24)
(8,0)
(24,0)
I first graphed the points. The axis of symmetry was given in the graph. Since I know the graph is a parabola and it has an axis of symmetry, the opposite side of the axis is reflected.
.