← LabsMath 1 · quadratics-parabolas

Parabola sliders

Vertex form vs standard; what D < 0 looks like.

b-2

c-3

Standard form

y = x^2 - 2x - 3

Vertex form

y = (x - 1)^2 - 4

vertex (1, -4)

Discriminant

D = b^2 - 4ac = 16

D > 0: two real roots, x = -1 and x = 3

Ring: the vertex. Dots: where y = 0. Slide c until the dots vanish and watch the sign of D.