# What is the vertex of #y=x^2-x+9-2(x-3)^2 #?

##### 3 Answers

#### Explanation:

Simplify to

Use FOIL to expand

Combine like terms

Now that we have turned the equation to

Let's turn them to

To make perfect square like

We know the formula that when

So

Substitute those values and let's find

Substitute

Therefore, we have turned the equation to

#### Explanation:

This equation looks scary, which makes it hard to work with. So, what we're gonna do is simplify it as far as we can and then use a small part of the quadratic formula to find the

Let's start with simplifying this equation:

At the end, there's this part:

Which we can factor to

When we distribute that

Put that back into the original equation and we get:

However, we can simplify it down to something very recognizable:

Now comes the cool part:

A small piece of the quadratic formula called the vertex equation can tell us the x-value of the vertex. That piece is

Our

We come out with

With knowing

Which goes to:

Which goes to:

Pair that with the

Vertex

#### Explanation:

Given -

#y=x^2-x+9-2(x-3)^2#

#y=x^2-x+9-2(x^2-6x+9)#

#y=x^2-x+9-2x^2+12x-18#

#y=-x^2+11x-9#

Vertex

#x=(-b)/(2a)=(-11)/(2 xx(-1))=11/2#

#y=-(11/2)^2+11((11)/2)-9#

#y=-121/4+121/2-9=(-121+242-36)/4=85/4#

Vertex