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Formula
Graph
$y = \left ( 2 + \sqrt{ 3 } \right ) x ^ { 2 } - \left ( 3 + \sqrt{ 3 } \right ) x + 1$
$y = 0$
$x$Intercept
$\left ( 1 , 0 \right )$, $\left ( 2 - \sqrt{ 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , 1 \right )$
Minimum
$\left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 3 } } { 2 } , - \dfrac { 7 } { 2 } - \sqrt{ 3 } \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 3 } } { 2 } \right ) + \sqrt{ 3 } \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 3 } } { 2 } \right ) ^ { 2 } + 2 \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 3 } } { 2 } \right ) ^ { 2 } + \dfrac { 3 \sqrt{ 3 } } { 2 } \right )$
Standard form
$y = \left ( \sqrt{ 3 } + 2 \right ) \left ( x + \left ( - \dfrac { 3 } { 2 } + \dfrac { \sqrt{ 3 } } { 2 } \right ) \right ) ^ { 2 } + \left ( - \dfrac { 7 } { 2 } - \sqrt{ 3 } \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 3 } } { 2 } \right ) + \sqrt{ 3 } \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 3 } } { 2 } \right ) ^ { 2 } + 2 \left ( \dfrac { 3 } { 2 } - \dfrac { \sqrt{ 3 } } { 2 } \right ) ^ { 2 } + \dfrac { 3 \sqrt{ 3 } } { 2 } \right )$
$\left( 2+ \sqrt{ 3 } \right) x ^{ 2 } - \left( 3+ \sqrt{ 3 } \right) x+1 = 0$
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