Question 1062085
The y-intercept occurs where {{{ x = 0 }}}, so
the y-intercept is {{{ y(0) }}}
{{{ y(0) = a*0^2 + b*0 + c }}}
{{{ y(0) = c }}}
{{{ c = -4 }}}
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( -2,8 )
{{{ y = a*x^2 + b*x - 4 }}}
{{{ 8 = a*(-2)^2 + b*(-2) - 4 }}}
{{{ 8 = 4a - 2b - 4 }}}
{{{ 4a - 2b = 12 }}}
(1) {{{ 2a - b = 6 }}}
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( 1, -2 )
{{{ y = a*x^2 + b*x - 4 }}}
{{{ -2 = a*1^2 + b*1 - 4 }}}
{{{ -2 = a + b - 4 }}}
(2) {{{ a + b = 2 }}}
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Add (1) and (2)
(1) {{{ 2a - b = 6 }}}
(2) {{{ a + b = 2 }}}
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{{{ 3a = 8 }}}
{{{ a = 8/3 }}}
and
(2) {{{ a + b = 2 }}}
(2) {{{ 8/3 + b = 2 }}}
(2) {{{ b = 6/3 - 8/3 }}}
(2) {{{ b = -2/3 }}}
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The equation is:
{{{ y = (8/3)*x^2 - (2/3)*x - 4 }}}
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check:
( -2,8 )
{{{ y = (8/3)*x^2 - (2/3)*x - 4 }}}
{{{ 8 = (8/3)*(-2)^2 - (2/3)*(-2) - 4 }}}
{{{ 24 = 8*4 + 4 - 12 }}}
{{{ 24 = 32 - 8 }}}
{{{ 24 = 24 }}}
OK
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(1,-2)
{{{ y = (8/3)*x^2 - (2/3)*x - 4 }}}
{{{ -2 = (8/3)*1^2 - (2/3)*1 - 4 }}}
{{{ -2 = 8/3 - 2/3 - 4 }}}
{{{ -6 = 8 - 2 - 12 }}}
{{{ -6 = 8 - 14 }}}
{{{ -6 = -6 }}}
OK