Quadratic Explorer

Quadratic Explorer — Graph y = ax² + bx + c Interactively

A quadratic is the first curve most students meet, and this explorer makes every coefficient tangible. Drag a, b, and c and the parabola y = ax² + bx + c redraws instantly, with the vertex, axis of symmetry, and roots marked. Watch the discriminant b² − 4ac decide whether the curve crosses the x-axis twice, touches it once, or misses it entirely.

What you can do in this simulation

• Adjust a, b, and c with sliders and see the parabola update live
• Track the vertex and the dashed axis of symmetry as the curve moves
• See the real roots marked where the parabola crosses the x-axis
• Read the discriminant and how it sets the number of real roots
• Connect the marked roots to the quadratic formula's two solutions

Concepts covered

quadratic function · parabola · vertex · axis of symmetry · roots · discriminant · quadratic formula

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