### Video Transcript

What is the vertex form of the function ๐ of ๐ฅ equals negative ๐ฅ squared plus six ๐ฅ plus five?

In order to put this function into the vertex form, we need to complete the square. And our first step is to group the first two terms together. And then, we need to make the leading coefficient a positive one and since thereโs a negative, we should take that out. And now that weโve done that, once weโve taken out the negative from negative ๐ฅ squared, that turns into positive ๐ฅ squared. And when we take out a negative from six ๐ฅ, that makes it negative six ๐ฅ.

So now, we need to work with a formula. So ๐ is our leading coefficient โ itโs one โ ๐ is negative six, and ๐ is five. And we need to take ๐ divided by two and square it. So we plug in negative six for ๐ and negative six divided by two is negative three and negative three squared is nine. And what we will do with the nine is to add to the inside of the parenthesis. But we have to keep the equation balanced. So since there is a negative upfront, technically this is a negative nine. So if we technically added in a negative nine to the equation, we need to add in a positive nine to counter it so that way it stays balanced, which weโve done here.

So we call it completing the square because we should create something that is squared. And inside the parenthesis is actually going to be something squared. Two numbers that multiply to be nine and add to be negative six are negative three and negative three. So we can replace whatโs in the parenthesis with ๐ฅ minus three times ๐ฅ minus three. And we can rewrite that as ๐ฅ minus three squared. And then, five plus nine on the outside is 14.

And now, weโre in vertex form. So ๐ of ๐ฅ equals negative ๐ฅ minus three squared plus 14 will be our final answer. And the reason they call this the vertex form is because these numbers will represent where the vertex would be. And itโs three for ๐ฅ because itโs ๐ฅ minus and then whatever we plug in. So ๐ฅ would be three and ๐ฆ would be 14. So the vertex of this function if it were graphed will be at three, 14.