Quadratic Formula Solver

Roots, vertex & axis of symmetry for ax²+bx+c

Grades HS

High School · Solve ax² + bx + c = 0

1x^2 + (-3)x + (2) = 0

a (x²)

b (x)

c (constant)

Examples:

Step 1 — Compute Discriminant

D = b^2 - 4ac = (-3)^2 - 4 \cdot 1 \cdot 2 = 9 - 8 = 1

D = 1 → Two distinct real roots (D > 0)

Step 2 — Apply Quadratic Formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{3 \pm \sqrt{1}}{2}

Step 3 — Roots

x_1 = 2, \quad x_2 = 1

Factored Form

(x - 2)(x - 1) = 0

Vertex

(3/2, -1/4)

\tfrac{-b}{2a} = \tfrac{3}{2}

Axis of Symmetry

x = 3/2

vertical dashed line

Y-intercept

(0, 2)

f(0) = c