Parabola Studio — Drag a Degree-2 Polynomial

Drag the white ● vertex · drag the gold ● focus · arrow keys nudge the selected handle · Shift = fine step

a ≈ 0 — the quadratic is becoming linear

Standard form · y = ax² + bx + c

y = 1·x² + 0·x + 0

a = 1.000 · b = 0.000 · c = 0.000

Vertex form · y = a(x − h)² + k

y = 1(x − 0)² + 0

vertex (0.00, 0.00) · axis x = 0.00

Roots & conic geometry

x = 0 (double root)

discriminant b² − 4ac = 0.000

focus (0.00, 0.25)

directrix y = −0.25

Overlays

Roots

Focus / directrix

Axis of symmetry

1-unit grid

Preset tour

y = x² opening up · a = 1

y = −x² opening down · a = −1

y = 0.5x² wider opening · a = 0.5

y = 2(x−3)²+2 shifted · narrow

y = −0.5(x−2)²+1 completed-state fixture · vertex (2, 1) · focus (2, 0.5)

Actions

Reset to y = x²

Replay tour

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Legend

vertex

focus

directrix

parabola

root