Quadratic Formula — FAQ
Frequently asked questions about Quadratic Formula ((-b±√Δ)/2a).
Q1. What does the discriminant (b²−4ac) tell me?
If it's positive, there are two real roots. If it equals zero, there's exactly one root (the vertex touches zero). If negative, there are no real roots — the parabola doesn't cross the x-axis.
Q2. Why does the parabola flip when a is negative?
A negative coefficient a means the parabola opens downward (like a frown). Positive a opens it upward (like a smile). This is why the sign of a determines whether the vertex is a minimum or maximum.
Q3. Where is the quadratic formula used in real life?
Projectile motion in physics, profit maximization in economics, signal processing in engineering, and lens curvature in optics all rely on solving quadratic equations.
Have more questions? Try the interactive calculator at /tools/quadratic-formula-visualizer