Discriminant Cases Move the slider — does the parabola hit the x-axis once, twice, or not at all? y = x² + c x y −4 −2 2 4 −4 −2 2 4 6 8 10 DISCRIMINANT D = 0 D = b² − 4ac SLIDER c = 0 CASE D = 0 One real root (tangent to x-axis) ROOTS x = 0 The discriminant tells you how many times the parabola crosses the x-axis. D > 0: two roots. D = 0: one root. D < 0: no real roots.
−4 +4