Quadratic Workbook

Explore standard and vertex forms — move the sliders to see how coefficients shape the parabola.

Active form

Standard form

f(x) = x²

Vertex form

f(x) = x²

a — opens up/down, width 1

b — shifts vertex left/right 0

c — y-intercept 0

Coefficient relationships

Vertex

(0, 0)

y-intercept

(0, 0)

x-intercepts (roots)

x = 0

Opens

upward

Axis of symmetry

x = 0

Want to see the algebra behind converting between these two forms?

See where quadratics show up in the real world — from game physics to satellite dishes.