Question 1126205
( 3, -73 )
{{{ y = a*x^2 + b*x + c }}}
{{{ -73 = a*3^2 + b*3 + c }}}
(1) {{{ 9a + 3b = -c - 73 }}}
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(-2, 2 )
{{{ 2 = a*(-2)^2 + b*(-2) + c }}}
(2) {{{ 4a - 2b = -c + 2 }}}
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(-2,2 )
The x-value of vertex is at:
{{{ x[v] = -b/(2a) }}}
{{{ -2 = -b/(2a) }}}
{{{ -b = -4a }}}
{{{ b = 4a }}}
Plug this back into (1) and (2)
(1) {{{ 9a + 3*(4a) = -c - 73 }}}
(1) {{{ 9a + 12a = -c - 73 }}}
(1) {{{ 21a + c = - 73 }}}
and
(2) {{{ 4a - 2*(4a) = -c + 2 }}}
(2) {{{ 4a - 8a + c = 2 }}}
(2) {{{ -4a + c = 2 }}}
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subtract (2) from (1)
{{{ 25a = -75 }}}
{{{ a = -3 }}}
and
{{{ b = 4a }}}
{{{ b = -12 }}}
and
(2) {{{ -4*(-3) + c = 2 }}}
(2) {{{ 12 + c = 2 }}}
(2) {{{ c = -10 }}}
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the equation is:
{{{ y = -3x^2 - 12x - 10 }}}
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check:
( 3, -73 )
{{{ -73 = -3*3^2 - 12*3 - 10 }}}
{{{ -73 = -27 - 36 - 10 }}}
{{{ -73 = -73 }}}
and
( -2,2 )
{{{ 2 = -3*(-2)^2 - 12*(-2) - 10 }}}
{{{ 2 = -3*4 + 24 - 10 }}}
{{{ 2 = -12 + 24 - 10 }}}
{{{ 2 = 2 }}}
OK