# How do you find the vertex of the parabola: #y=x^2+2x+2#?

##### 1 Answer

Vertex:

#### Explanation:

There are two methods to solve this:

**Method 1** : Converting to Vertex Form

Vertex form can be represented as

where the point

To do that, we should complete the square

First, we should try to change the last number in a way

so we can factor the entire thing

to make it look like

If you notice, the only difference between the original

[Since we can't randomly change the 2 to a 1, we can add 1 and subtract a 1 to the equation at the same time to keep it balanced.]

[ *So we get...* ]

[ *Organizing...* ]

[ *Add like terms.. 2-1=1* ]

[ *Factor! :)* ]

Now comparing it to

We can see that the vertex would be

**-----.:.-----**

**Method 2** : Axis of Symmetry

The axis of symmetry of a quadratic equation aka parabola is represented by

Now in this case of

we can determine that

plugging this into the

we get

therefore the x point of the vertex would be

to find the y point of the vertex all we have to do is plug

we would get:

simplify:

therefore the y point of the vertex would be

with these two pieces of information,

would become