How to use
To change the values of the coefficients, use the "+"
and "-" buttons
under each value. The buttons change the value by 0.1 at each step.
Holding a button down causes this action to be repeated.
Click the "Clear" button to reset all values
to the default values, a=1 and all other values are 0.
Examples
Horizontal shifts:
in standard form, a=1, k=0 h=
-2,
-1,
0,
1,
2
Vertical shifts:
in standard form, a=1, h=0 k=
-2,
-1,
0,
1,
2
Effect of changing b:
in general form, a=1, c=1 b=
-2,
-1,
0,
1,
2
Other Notes
Notice how changes in the coefficients in one form
of the equation affect the coefficients in the other form.
The coefficient a takes the same value in both forms.
The coordinates of the vertex (h,k)
as in the standard form equation can be determined from
the coefficients a, b, and c of the general form
equation by the following formulas:
h=-b/2a,
k=c-b^{2}/4a.
The coefficients b and c in the general form equation
can be determined from the coordinates of the vertex (h,k)
as in the standard form equation, along with the
common coefficient a, by the following formulas:
b=-2ah,
c=k+ah^{2}.