The equation of which graph has a negative discriminant?

Question

A. The graph shows a parabola opening up with a vertex at 2 comma negative 1

 

B. The graph shows a parabola opening up with a vertex at negative 1 comma negative 3

 

C. The graph shows a parabola opening down with a vertex at negative 1 comma negative 1

 

D. The graph shows a parabola opening down with a vertex at negative 1 comma 0

Answer 1

If the discriminant is negative, that means that the roots of the quadratic function are not real numbers.  In other words, the graph has no x-intercepts.  Of the four choices that are given, choices (B) and (C) are both possible.    

Answer 2

If the discriminant is negative the roots are complex. Therefore the parabola does not intersect the x-axis. Select the option that describes a parabola that does not intersect the x-axis.