Question 615709
y = -(x + 2)² + 2
<pre>
Learn the following:

y = A(x - H)² + K 

is the equation of a curve called a parabola, that either looks like this

{{{graph(15,15,8.5,11,10,11,(x-10)^2+10)}}} or like this: {{{graph(15,15,8.5,11,9,10,-(x-10)^2+10)}}}

If it looks like this {{{graph(15,15,8.5,11,10,11,(x-10)^2+10)}}}, we say it OPENS UPWARD

If it looks like this {{{graph(15,15,8.5,11,9,10,-(x-10)^2+10)}}}, we say it OPENS DOWNWARD
 

The turning point (called the "vertex") is at the bottom of the graph
if it looks like this {{{graph(15,15,8.5,11,10,11,(x-10)^2+10)}}} 

The turning point or vertex is at the top of the graph if it looks 
like this {{{graph(15,15,8.5,11,9,10,-(x-10)^2+10)}}}.

The vertex is the point (H,K).

If A, the coefficient of the parentheses, is positive, the graph will
look like this: {{{graph(15,15,8.5,11,10,11,(x-10)^2+10)}}}

If A, the coefficient of the parentheses, is negative, the graph will
look like this: {{{graph(15,15,8.5,11,9,10,-(x-10)^2+10)}}}.

Two points on each side of the vertex which the parabola goes through
are (H-1,K+A) and (H+1,K+A)



Now let's compare your equation:

y = -(x + 2)² + 2

with this one:

 y =  A(x - H)² + K

Put a 1 between the negative sign and the parentheses:

 y = -1(x + 2)² + 2

You can see that A = -1, 

You can see that -H = +2, and so H = -2

You can see that K = 2

Therefore the vertex (turning point) is (H,K) = (-2,2)

Since A is a negative number the parabola open downward and so it will
look like this: {{{graph(15,15,8.5,11,9,10,-(x-10)^2+10)}}}

Two other points are (H-1,K+A) and (H+1,K+A).
These are 

(H-1,K+A) = (-2-1,2-1) = (-3,1) 

and 

(H+1,K+A = (-2+1,2-1) = (-1,1)

So we plot those three points, the vertex (-2,2), and the two points
(-3,1) and (-1,1), like this::

{{{drawing(400,400,-7,3,-5,5,graph(400,400,-7,3,-5,5),
circle(-2,2,.05), circle(-1,1,.05), circle(-3,1,.05) )}}}

Then we can sketch in the graph:

{{{drawing(400,400,-7,3,-5,5,graph(400,400,-7,3,-5,5,-(x+2)^2+2),
circle(-2,2,.05), circle(-1,1,.05), circle(-3,1,.05) )}}}

It has the axis of symmetry, which is a vertical line through the
vertex, which has the equation 

x = H

 which in your case is the equation 

x = -2, 

and is the green vertical line below that goes through
x = -2 on the x-axis:

 {{{drawing(400,400,-7,3,-5,5,graph(400,400,-7,3,-5,5,-(x+2)^2+2),
circle(-2,2,.05), circle(-1,1,.05), circle(-3,1,.05), green(line(-2,-10,-2,10)) )}}}

Edwin</pre>