# Question #5508c

##### 1 Answer

Note that the parabola's vertex is at the point

graph{6(x+3)^2 - 53 = y [-10, 10, -5, 5]}

#### Explanation:

A quadratic is in **vertex form** when it is something like this:

It is so named because the point

The easiest way to get into vertex form is to use the method of **completing the square**. This essentially means you add something to this polynomial to make it a perfect square.

**Step 1: Factor Out Leading Coefficient**

So we'd have to factor out a 6 here, which would leave us with:

**Step 2: What to add?**

This is probably the hardest part of this entire process. You need to find something to add to that quadratic above to make it a perfect square. To do this, let's recall the expansion of a perfect square:

We know that

Yay! However, we need to add something that makes the quadratic above

However, note that this is what we're adding to the quadratic *inside the parenthesis*. Because everything in there is multiplied by *really* adding is

**Step 3: Actually Add**

Adding

But wait, are we just allowed to add numbers to one side of the equation? The answer is no! What we do to one side of the equation, we must do to the other side. Therefore, we'd add

**Step 3: Simplify**

Some quick cleanup gives:

We know that

Lastly, we just subtract 53 from both sides, to achieve our desired form:

And that is your final answer!

Useful Video:

Hope that helped :)