Find the discriminant.

b² − 4ac = 0² − 4(1)(−6) = 24

This equation has real roots.

b² − 4ac = 0² − 4(1)(6) = −24

This equation has complex roots.

See part (b).

This equation has complex roots.

See part (a).

Find the vertex.
Is it above or below the x-axis?

See part (e).