Assertion: parabola's equation | /r/HasAspect | real roots
Facets:
value: without computing the discriminant
type: MANNER
value: d 2 − 4
type: OTHER
value: if
type: DEGREE
Source sentences:
text: If the vertex is above the x x x-axis, then the parabola will not intersect the x x x-axis and the equation will have no real roots.
text: Applying a similar logic from the previous case, the equation will have two real roots if and only if the vertex is either on the x x x-axis or above it.
text: If the discriminant is positive, then the equation does have real roots: D = b 2 − 4 a c = ( − 2 ) 2 − 4 × 1 × ( − 4 ) = 4 + 16 = 20 > 0.
text: Since the discriminant is positive, we can conclude that the equation has real roots.
text: a > 0 a>0, we can say that the vertex must be below the x x x-axis and the equation will have real roots, without computing the discriminant.