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Angry birds quadratic project
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Transcript
Angry Birds Quadratic Project
Version 2
By: Charlie W
Vertex
Axis of symmetry
KEY
Yellow= Yellow Bird
Red= Red Bird
Black= Black Bird
Blue= Blue Bird
Vertex
Axis of symmetry
Vertex
Axis of symmetry
Graph
Calculations
completing the square
Red
0=-5/48x^2+5/2x
5/2/-5/48=-24 0/-5/48=0
0=x^2-24x
-24/2=-12^2=144
144=x^2-24x+144
(x-12)^2=144
sqr root(x-12)^2=sqr root144
x-12=(+or-)12
x-12=12
x=24
x-12=-12
x=0
x=0 or 24
distance
24-0=24 yards
v=12,15
xy table
x=6 y=11.25
6^2=36(-5/48)=-3.75+5/2(6)
15-3.75=11.25
Blue
v=(16,22)
22=a(16-6)(16-26)
10(-10)=-100
22=-100a
22/-100=-.22
y=-.22(x-6)(x-26)
xy table
x=10 y=14.08
10-6=4 10-26=-16
-16(4)=-64(-.22)=14.08
x intercepts given are 6 and 26
distance traveled 26-6= 20 yards
Quadratic Formula
Roots
y=-x^(2)+16x-39
y=ax^(2)+bx+c
{-b(+or-) sqr root[b^(2)-4(a)(c)}/2(a)
{-16(+or-) sqr root[16^(2)-4(-1)(-39)}/2(-1)
{-16(+or-) sqr root[256-156]}/-2
{-16(+or-) sqr root[100]}/-2
{-16(+or-) 10}/-2
-16+10=-6/-2=3
-16-10=-26/-2=13
x= 3 or 13
13-3=10 distance traveled
Vertex
-16/2(-1)=8
8^2=64
-64+16(8)-39=25
vertex=(8,25)
xy table
x=7 y=24
7^2=49
-49+16(7)-39=24
axis of symmetry: x= 25
Black
Factoring
Yellow
x int=12 and 24
point 13,11
v=18,36
y=a(x-p)(x-q)
11=a(13-12)(13-24)
11=a(1)(-11)
11=-11a
a=-1
y=-1(x-12)(x-24)
y=-1(x^(2)-12x-24x+288)
y=-x^(2)+36x-288
36/-1 -288/-1
x^2-36x+288
magic number
288*1=288
x^2-24x-12x+288
(x^2-24x)(-12x+288)
(x^2-24x)=x(x-24)
(-12x+288)=-12(x-24)
(x-12)(x-24)
x=12 or 24
distance traveled
24-12=12 yards
Highest: Yellow
Longest: Red
King Pig hit by: Yellow
Mustache Pig hit by: Black
Data
Red
Max Height: 15 Yards
Axis of symmetry: x=12
Distance traveled: 24 Yards
Equation: y=-5/48x+5/2x
Max Height: 25 yards
Axis of symmetry: x=8
Distance traveled: 10 Yards
Equation: y=-x^(2)+16x-39
Black
Blue
Max Height: 22 Yards
Axis of symmetry: x=16
Distance traveled: 20 Yards
Equation: y=-.22x^(2)+7.04x-34.32
Max Height: 36 Yards
Axis of symmetry: x=18
Distance Traveled: 12 Yards
Equation: Y=-x^(2)+36x-288
Yellow
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