The formula for the vertex of a parabola, which
is the highest or lowest point, whose equation is:



First we calculate the discriminant

.

then the vertex is

(, ) 

Example:

For the parabola 



We can find a few points by selecting
arbitrary values for x, substituting
and finding the y-values.

For example, if we substitute 
into






So we have the point (-1,5)

We can find others the same way.

I found (-3,-7), (-1,5), (0,8), (3,5), and (5,-7).

Let's plot those:



We compare this problem:



to



and find , , 

To find the vertex, we first calculate the discriminant

.

then the vertex is

(, ) =

(, ) =

(, ) =

(, ) =

So we plot the vertex at (, )



and sketch in the parabola:



Edwin