# What is the vertex form of #y= 6x^2 + 20x + 6 #?

##### 2 Answers

**Vertex form of equation is**

#### Explanation:

Vertex form of equation is

subtracted simultaneously to make a square]

So vertex is at

#### Explanation:

Let's start by recognizing the general *vertex form* which will be our target:

Given

We will first separate the

then extract the

To "complete the square" fro the

In this case since we already have

the value of

and

we will need to add

Obviously, if we are going to add an amount someplace we will need to subtract it someplace else to keep everything equal to the original expression.

...but how much do we need to subtract?

If we look carefully we see that we will not just be adding **times** the

So we will need to subtract

We now have:

If we re-write the parenthesized component as a squared binomial and simplify the constants we get

or, in explicit *vertex form*

The graph below of the original equation indicates that this answer is "reasonable" (although I haven't figured out how to capture it with the vertex coordinates displayed)

graph{6x^2+20x+6 [-5.582, 2.214, -11.49, -7.593]}