Parabola of the Form y=x²+c: Linking function properties to its representation

Find the corresponding algebraic representation for the function

$y=x^2-6$

Find the corresponding algebraic representation for the function

$y=-x^2+1$

Find the corresponding algebraic representation for the function

$y=x^2$

Find the corresponding algebraic representation for the function

$y=x^2-2$

Find the corresponding algebraic representation for the function

$y=-x^2+6$

Find the corresponding algebraic representation for the function

$y=-x^2-2$

Find the corresponding algebraic representation for the function

$y=x^2+5$