Question 914911
{{{ y = 2x^2 + 8x + 5 }}}
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{{{ y = a*( x-h )^2 + k }}}
{{{ y = a*( x^2 - 2h*x + h^2 ) + k }}}
{{{ y = a*x^2 - 2a*h*x + a*h^2 + k }}}
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From this, I get:
(1) {{{ a = 2 }}}
(2) {{{ -2a*h = 8 }}}
(3) {{{ a*h^2 + k = 5 }}}
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Substitute (1) into (2)
(2) {{{ -2*2*h = 8 }}}
(2) {{{ h = -2 }}}
and
(3) {{{ 2*(-2)^2 + k = 5 }}}
(3) {{{ 8 + k = 5 }}}
(3) {{{ k = -3 }}}
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So, the answer is:
{{{ y = 2*( x-(-2) )^2 - 3 }}}
{{{ y = 2*( x+2 )^2 - 3 }}}
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Check answer:
{{{ y = 2*( x^2 + 4x + 4 ) - 3 }}}
{{{ y = 2x^2 + 8x + 8 - 3 }}}
{{{ y = 2x^2 + 8x + 5 }}}
OK