Question 816426: How do you write an equation for an upside down parabola going through points (0,0) (24,12) and (32,0)?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How do you write an equation for an upside down parabola going through points (0,0) (24,12) and (32,0)?
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Set up a system of 3-equations using form y=Ax^2+Bx+C
(0,0) 0=0+0+C
C=0
(24,12) 12=24^2A+24B+0
(32,0) 0=32^2A+32B+O
..
384=32*24^2A+768B+0
0=24*32^2A+768B+0
..
384=18432A+768B+0
0=24576A+768B+0
subtract:
384=-6144A
A=-6144/384=-1/16
32B=-32^2A=-32^2*-1/16=64
B=2
Equation:
y=-x^2/16+2x
complete the square:
y=(-1/16)(x^2-32+256)+16
y=(-1/16)(x-16)^2+16
This is an equation of a parabola of the form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of center.
For given parabola:
vertex: (16,16)
A=-1/16
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