Parabolas

Graphs a parabola, showing coefficients for the equation in both standard form, y=a(x-h)2+k, and general form, y=ax2+bx+c.
How to use   ||   Examples   ||   Other Notes


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-b2/4a. 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+ah2.