b2KIT

Quadratic Equation Solver

Solve quadratic equations using the quadratic formula with step-by-step solutions, discriminant analysis, and graphing.

Equation

x² -5x + 6 = 0

Coefficients: ax² + bx + c = 0

Root 1 (x₁)

3

Root 2 (x₂)

2

Discriminant

1

Root Type

real distinct

Vertex

(2.5, -0.25)

Axis of Sym.

x = 2.5

Step-by-Step Solution

•Given: 1x^2 + -5x + 6 = 0
→Discriminant = b^2 - 4ac = -5^2 - 4(1)(6) = 1
→Discriminant > 0: Two distinct real roots
→sqrt(1) = 1
→x1 = (-b + sqrt(D)) / 2a = (5 + 1) / 2 = 3
→x2 = (-b - sqrt(D)) / 2a = (5 - 1) / 2 = 2
•Vertex form: y = 1(x - 2.5)^2 + -0.25
•Vertex: (2.5, -0.25)
•Axis of symmetry: x = 2.5
•Opens upward

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

Part of the upcoming MAPb2 suite -- Visual Thinking Tools

How to Use Quadratic Equation Solver

  1. 1

    Enter coefficients

    Type the values for a, b, and c in the equation.

  2. 2

    Solve the equation

    Click solve to find the roots of the quadratic equation.

  3. 3

    View the solution

    See both roots, discriminant value, and the solution steps.

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