Quadratics That Are Always Positive or Always Negative

D=b2-4ac (a 0) Conditions for all real values of x **Statement** | **y=ax2+bx+c** | **y=a(x-h)2+k** | **Sketch** Always positive: y>0 for all real x | a>0 and b2-4ac<0 | a>0 and k>0 | Always negative: y<0 for all real x | a<0 and b2-4ac<0 | a<0 and k<0 | Never negative: y >= 0 for all real x | a>0 and b2-4ac <= 0 | a>0 and k >= 0 | Never positive: y <= 0 for all real x | a<0 and b2-4ac <= 0 | a<0 and k <= 0 |