Interactive parabola

Drag the sliders and see the parabola change in real time. The quadratic formula is solved step by step with your numbers.

The quadratic function:

f(x) = ax² + bx + c

a = opening direction (+ up, - down) · b = horizontal position · c = y-intercept

a — opening direction

b — horizontal position

c — y-intercept

-4

Function

          f(x) = x² - 4
        

Vertex

x = 0, y = -4

Discriminant D = b²-4ac

D = 16

Zeros / roots

x = -2, x = 2

Remember the discriminant:
D > 0 → two zeros · D = 0 → one zero (touches x-axis) · D < 0 → no real zeros

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.

— William Paul Thurston (1946–2012)