π Mathematics
Quadratic graph
Move a parabola with a, b and c.
Quadratic graph
💬 Questions and answers
1What am I looking at?
Answer: The parabola y = ax² + bx + c on a grid.
2What are its parts? (click a part to identify it)
Answer: The curve, the x-axis crossings (roots), the vertex and the coefficients a, b and c.
3How does it work?
Answer: The sign of a decides whether the parabola opens up or down; the discriminant D = b² − 4ac decides how many times it meets the x-axis.
4Why is it important?
Answer: Quadratics model projectiles, areas, profits and many real situations.
5What happens if I change something? (use the sliders)
Answer: Change a, b and c and watch the roots appear, merge and disappear.
6What should I remember for the exam?
Answer: Roots x = (−b ± √D) ÷ 2a. D > 0: two real roots; D = 0: equal roots; D < 0: no real roots. Vertex at x = −b ÷ 2a.