Vertex Form Explorer
Manipulate parameters to understand quadratic transformations.
Input Mode
Vertex (a,h,k)
Standard (a,b,c)
Stretch / Reflection (a)
{{ params.a.toFixed(1) }}
Horizontal Shift (h)
{{ params.h.toFixed(1) }}
Linear Coeff (b)
{{ params.b.toFixed(1) }}
Vertical Shift (k)
{{ params.k.toFixed(1) }}
Constant (c)
{{ params.c.toFixed(1) }}
Display Options
Ref: y=x²
Vertex
Axis of Sym.
Roots
Vertex
{{ vertex.x.toFixed(2) }}, {{ vertex.y.toFixed(2) }}
Axis of Symmetry
x = {{ vertex.x.toFixed(2) }}
Discriminant (D)
{{ discriminant.toFixed(2) }}
Real Roots
{{ roots.length }} point(s)
Coefficients
b = {{ params.b.toFixed(2) }}, c = {{ params.c.toFixed(2) }}
$$ y = ... $$