Quadratic Formula Calculator

Your details

Choose which form your equation is already in.
The coefficient of x^2. Must not be zero.
The coefficient of x.
The constant (free) term.
Also display the equation rewritten in vertex form and factored form.
x1
2
x21
Discriminant (b^2 - 4ac)1
Vertex (h, k)(1.5, -0.25)
Axis of symmetryx = 1.5
Sum of roots (Vieta)3
Product of roots (Vieta)2
Sum of roots3
Product of roots2
Discriminant1

Discriminant = 1: two distinct real roots.

  • The discriminant is 1, giving two distinct real roots.
  • The parabola has its vertex at (1.5, -0.25), which is its minimum (if a > 0, opens up) or maximum (if a < 0, opens down) point.
  • By Vieta's formulas, the roots always sum to 3 and multiply to 2, a quick sanity check without solving.
  • Substitute a root back into ax^2 + bx + c to verify it gives zero.

Next stepSubstitute each root into the original equation to confirm both sides equal zero.

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