graph the parabola. find the vertex.

y = 2(x + 3)(x - 1)

Multiply using FOIL

y = 2(x² - x + 3x - 3)

Combine like terms:

y = 2(x² + 2x - 3)

Distribute to remove parentheses:

y = 2x² + 4x - 6

Factor coefficient of x² out of first
two terms only:

y = 2(x² + 2x) - 6

On scratch paper, 

multiply the coefficient
of x inside the parentheses, which is -2,
by one-half (always 1/2):

-2 times 1/2 equals -1

Now, still on scratch paper, square -1.
(-1)² = -1 times -1 equals +1, so add 1,
then subtract 1 inside the parentheses,
like this:

y = 2(x² + 2x + 1 - 1) - 6

This does not change the value because
adding 1 and then subtracting 1 amounts 
to adding 0.

Change the parentheses to brackets because
we are going to have parentheses inside of
parentheses next:

y = 2[x² + 2x + 1 - 1] - 6

Now factor the first three terms inside the 
brackets as a trinomial:

y = 2[(x+1)(x+1) - 1] - 6
 
Notice that the two factors are exactly
alike so we can write (x+1)(x+1) as (x+1)²

y = 2[(x+1)² - 1] - 6

Now remove the brackets by distributing.
Multiply the 2 by the (x+1)² leaving the 
(x+1)² intact, then multiply the 2 by 
the -1

y = 2(x+1)² - 2 - 6

Combine the -2 and the -6 as -8

y = 2(x+1)² - 8

Now it is in the standard form:

y = a(x-h)² + k

where a = 2, h = -1 and k = -8

The vertex is the point (h,k) = (-1,-8)

It also goes through the points

(h-1,k+a) and (h+1,k+a)

which are

(-1-1, -8+2) and (-1+1, -8+2)

or

(-2, -6) and (0, -6)

So the graph looks like this:



Edwin