# How do you find the vertex of #y=x^2+4x+1#?

##### 1 Answer

The vertex is

#### Explanation:

*Note: when the variables a, b, c, etc. are used, I am referring to a general rule that will work for every real value of a, b, c, etc.*

**The vertex can be found in many ways:**

**The simplest is using a graphing calculator** and finding the vertex that way- but I assume you mean how to calculate it **mathematically**:

In an equation

Using the equation

You can then plug that into the equation and solve for the y value of the vertex:

Therefore, the answer is

**Alternatively, you can solve by completing the square:**

with

You have

I did this because

You can then subtract 4 from both sides to isolate

With the form

graph{y=x^2+4x+1 [-10, 10, -5, 5]}

Hope this helps!