Quadratic
Workbook
Explore standard and vertex forms — move the sliders to see how coefficients shape the parabola.
Active form
Standard f(x) = ax² + bx + c
Vertex f(x) = a(x−h)² + k
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
a
— opens up/down, width
1
h
— vertex x-position
0
k
— vertex y-position
0
Coefficient relationships
Vertex
(0, 0)
y-intercept
(0, 0)
x-intercepts (roots)
x = 0
Opens
upward
Axis of symmetry
x = 0