Question 1127572
The general formula is:
{{{ y = a*x^2 + b*x + c }}}
( 3,0 )
( 9,0 )
( 10,-7 )
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( 3,0 )
{{{ 0 = a*3^2 + b*3 + c }}}
(1) {{{ 9a + 3b + c = 0 }}}
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(9,0)
{{{ 0 = a*9^2 + b*9 + c }}}
(2) {{{ 81a + 9b + c = 0 }}}
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( 10,-7 )
{{{ -7 = a*10^2 + b*10 + c }}}
(3) {{{ 100a + 10b + c + 7 = 0 }}}
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Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
{{{ 54a - 3c = 0 }}}
{{{ c = 18a }}}
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Plug this result into (3)
(3) {{{ 100a + 10b + 18a + 7 = 0 }}}
(3) {{{ 118a = -10b - 7 }}}
(3) {{{ 10b = -118a - 7 }}}
(3) {{{ b = (1/10)*( -118a - 7 ) }}}
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You can plug c and b back into (1) and
find a
Will let you finish