Answer
$y=\pm 2\sqrt {3\left( 1-x^{2}\right) }$
Work Step by Step
$x^{2}+\dfrac {y^{2}}{12}=1\Rightarrow \dfrac {y^{2}}{12}=1-x^{2}\Rightarrow y^{2}=12\left( 1-x^{2}\right) \Rightarrow y=\pm \sqrt {12\left( 1-x^{2}\right) }=\pm 2\sqrt {3\left( 1-x^{2}\right) }$
Now we can graph this equation using graphing calculator as asked in question