Second form of parabola, Algebra

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As noted earlier most parabolas are not given in that form.  So, we have to take a look at how to graph a parabola which is in the general form.

                                          f ( x ) = ax2 + bx + c

In this the sign of a will find out whether or not the parabola will open upwards or downwards.  Not like the previous form we will not obtain the vertex for free this time.  Though, it is will simple to determine. following is the vertex for a parabola in the general form.

                                                             ( - b /2a , f (- b /2a))

To obtain the vertex all we do is calculate the x coordinate from a & b and then plug this into the function to obtain the y coordinate. Not quite as easy as the earlier form, but yet not all that hard.

Note as well that we will obtain the y-intercept for free from this form.  The y-intercept is,

     f (0) = a (0)2  + b (0) + c = c           ⇒                   (0, c )

Thus we won't have to do any computations for this one.


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