Draw the graphs of the following parabolas :
(i) `x=y ^(2) - 2y -3`
(ii) `x = 6+y -y^(2)`

Explanation

(i) `x= y^(2) - 2y -3= (y-3)(y+1)`
or `" " x=(y-1)^(2) -4`
or `" "x+4=(y-1)^(2)`
Hence the vertex of the parabola is `(-4, 1)`, and the parabola opens to the right, intersecting the y-axis at `(0, -1) and (0, 3)`.

(ii) `x= 6+y -y^(2)`
or `" "x= -(y^(2)-y -6)`
`" "= -(y-3) (y+2)`
Hence the parabola opens to the left, intersects the y-axis at `(0, -2) and (0, 3)` and has vertex at `((25)/(4), -(1)/(2))`.