Question 919974
Parabola
{{{y=ax^2+bx+c}}}
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1.{{{5=a(0)+b(0)+c}}}
1.{{{c=5}}}
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2.{{{3=a(1)+b(1)+5}}}
2.{{{a+b=-2}}}
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3.{{{21=a(16)+b(4)+5}}}
3.{{{16a+4b=16}}}
3.{{{4a+b=4}}}
From eq. 2,
{{{a=-2-b}}}
Substituting,
{{{4(-2-b)+b=4}}}
{{{-8-4b+b=4}}}
{{{-3b=12}}}
{{{b=-4}}}
Then,
{{{a=-2-(-4)}}}
{{{a=2}}}
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{{{highlight_green(y=2x^2-4x+5)}}}
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Inverse parabola
{{{x=ay^2+by+c}}}
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4.{{{0=a(25)+b(5)+c}}}
4.{{{25a+5b+c=0}}}
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5.{{{1=a(9)+b(3)+c}}}
5.{{{9a+3b+c=1}}}
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6.{{{4=a(441)+b(21)+c}}}
6.{{{441a+21b+c=4}}}
Subtract eq. 5 from eq. 4 and eq. 6 to eliminate {{{c}}}
7.{{{25a+5b+c-(9a+3b+c)=0-1}}}
7.{{{16a+2b=-1}}}
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8.{{{441a+21b+c-(9a+3b+c)=4-1}}}
8.{{{432a+18b=3}}}
8.{{{144a+6b=1}}}
Multiply eq. 7 by -3 and add to eq. 8 to eliminate {{{b}}}
{{{144a+6b-48a-6b=1+3}}}
{{{96a=4}}}
{{{a=1/24}}}
Then,
{{{16(1/24)+2b=-1}}}
{{{2/3+2b=-1}}}
{{{2b=-5/3}}}
{{{b=-5/6}}}
Finally,
{{{9/24+3(-5/6)+c=1}}}
{{{9/24-60/24+c=24/24}}}
{{{c=75/24}}}
{{{c=25/8}}}
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{{{highlight_green(x=y^2/24-(5/6)y+25/8)}}}