Parabola y = ax² and quadratic equations

MathematicsFunctions & GraphsAges 14–15

The graph of y = ax² together with the line y = bx + c. Drag the point on the parabola to change a (opens up/down, narrow/wide), and drag the two points on the line to change b and c. The x-coordinates of the intersection points solve ax² − bx − c = 0: the discriminant Δ = b² + 4ac updates instantly, along with the number of intersections (0, 1, or 2) and the root formula.