Question 1

How do I solve a quadratic equation ax²+bx+c=0?

Accepted Answer

Use the quadratic formula x = (-b ± √(b²-4ac)) / (2a). First compute the discriminant D = b²-4ac. If D>0 there are two distinct real roots; if D=0 one repeated real root; if D<0 two complex conjugate roots.

Question 2

What is the discriminant of a quadratic?

Accepted Answer

The discriminant is D = b²-4ac. Its sign tells you the type of roots: D>0 means two distinct real roots, D=0 means exactly one real root (a repeated root), and D<0 means two complex conjugate roots.

Question 3

How do I find the vertex of a parabola?

Accepted Answer

For y = ax²+bx+c the vertex is at x = -b/(2a). Substitute back to get y = c - b²/(4a). The axis of symmetry is the vertical line x = -b/(2a). When a>0 the parabola opens upward and the vertex is the minimum; when a<0 it opens downward and the vertex is the maximum.

Question 4

Can this solver handle complex (imaginary) roots?

Accepted Answer

Yes. When the discriminant is negative the solver reports the two complex conjugate roots in the form p ± qi, where i is the imaginary unit.