Drag the vertex on canvas — toggle area shading, focus & directrix
Vertex form y = a(x−h)²+k shows the vertex at (h, k). When a > 0 the parabola opens up; a < 0 opens down. |a| controls width — larger |a| means narrower. The discriminant Δ = −4ak for vertex form tells you: Δ > 0 → 2 real roots, Δ = 0 → 1 root, Δ < 0 → no real roots. Toggle Shade Area to see the area between the curve and the x-axis between the roots. Drag the vertex directly on the canvas!