Quadratic Formula Calculator

Inputs

Results update as you type.

ax² + bx + c = 0
Graph of the parabola and its rootsx = 2 and x = 3vertex (2.5, -0.25)myconstructioncalculator.com
Diagram updates as you type.

Results

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Roots
x = 2 and x = 3
Discriminant (b² − 4ac)1
Type of rootsTwo real roots
Vertex (turning point)(2.5, −0.25)
Axis of symmetryx = 2.5
y-intercept(0, 6)
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Working
  1. Equation: x² − 5x + 6 = 0
  2. x = (−b ± √(b² − 4ac)) ÷ 2a
  3. b² − 4ac = (−5)² − 4 × 1 × 6 = 1
  4. x = (5 ± √1) ÷ 2 = (5 ± 1) ÷ 2, so x = 2 and x = 3
  5. Vertex at x = −b ÷ 2a = 2.5, y = −0.25

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