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In a Nutshell: Parabola Forms

part of the In a Nutshell series on Adrian’s Study Club

Factored form y=a(x-x_1)(x-x_2)


  1. 2 x-ints
  2. One other point `P(x,y)

Vertex Form y=a(x-h)^2 + k


  1. Vertex V(h,k)
  2. P(x, y)

General Form y=ax^2 + bx + c


  1. 3 points


  1. 2 points
  2. y-int where y-int = c


  1. Axis of symmetry `x=-(b/2a)
  2. 2 other points

Form General y = ax^-2 + bx + c Vertex y =a (x-h)^2 + k Intercept y=(x-x_1)(x-x_2)
Axis of symmetry x = -(b/2a) x = h x=((x_1 + x_2)/2)
Vertex Sub x = -(b/2a) into the equation to find y. (h, k) Sub x=((x_1 + x_2)/2) into the equation to find y.
Form Vertical Translation y = ax^2 + c Horizontal translation y=a(x-h)^2
Axis of symmetry x=0 (y-axis) x=h
Vertex V(O,c) V(h,0)

Parabola forms

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