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Quadratic Function : Parabola

Quadratic Function
Parabola: y - k = a(x - h)2, in which a = 1/(2p)
Vertex ( h, k)
Axis of symmetry: x = h
foci: ( h, k + p/2)
Directrix: y = k - p/2
Direction open upward if p > 0, open downward if p < 0
Parabola equation y = 0.25 x^2
y = 0.25 x2
Vertex (0, 0)
Axis of symmetry x = 0
foci ( 0, 1)
Directrix y = -1
Parabola equation y = - 0.25 x^2
y = - 0.25 x2
Vertex: (0, 0)
Axis of symmetry: x = 0
foci: ( 0, -1)
Directrix: y = 1
Open downward
Parabola equation y - 1 = 0.25( x - 2)^2
y - 1 = 0.25( x - 2)2
Vertex: (2, 1)
Axis of symmetry: x = 2
foci: (2, 2)
Directrx: y = 0
Open upward
Parabola equation y - 10 = -0.125( x - 2)^2
y - 10 = -0.125( x - 2)2
Vertex: (2, 10)
Axis of symmetry: x = 2
foci: (2, 8)
Directrx: y = 12
Open downward