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We now know that we have two basic types of parabolas: those which open up and down those which open left or right.

The table below looks at some similarities and differences between these two types of parabolas.

TYPE 1	TYPE 2
General Equation: By2 + Cx + Dy + F = 0	General Equation: Ax2 + Cx + Dy + F = 0
Standard Equation: x - h = a(y - k)2 or x = a(y - k)2 + h	Standard Equation: y - k = a(x - h)2 or y = a(x - h)2 + k
Look carefully at the positions of h and k in the standard equations above. Note: h is always associated with the x-variable. k is always associated with the y-variable.
Standard Equation with vertex at origin: x = y2	Standard Equation with vertex at origin: y = x2
No x2-term in the general or standard equations.	No y2-term in the general or standard equations.
Similarities: In the standard equation (h, k) represents the coordinates of the parabola's vertex. Varying h and k changes the position of the parabola. Varying h translates the parabola parallel to the x-axis. Varying k translates the parabola parallel to the y-axis. In the standard equation a affects the width of the parabola. As |a| increases, the parabola gets narrower. As |a| approaches zero, the parabola opens wider. If a = 0, the resulting graph is a straight line.