### Home > A2C > Chapter 9 > Lesson 9.2.2 > Problem 9-91

9-91.

Decide which of the following equations have real roots, and which have complex roots without completely solving them. Homework Help ✎

*y*=*x*^{2}− 6*y*=*x*^{2}+ 6*y*=*x*^{2}− 2*x*+ 10*y*=*x*^{2}− 2*x*− 10*y*= (*x*− 3)^{2}− 4*y*= (*x*− 3)^{2}+ 4

Find the discriminant.

*b*^{2} − 4*ac* = 0^{2} − 4(1)(−6) = 24

This equation has real roots.

*b*^{2} − 4*ac* = 0^{2} − 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).