what is the vertex of the graph of f(x) = |x + 5| – 6? (–6, –5) (–6, 5) (–5, –6) (5, –6) This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you Graphing a qudratic by converting to vertex form. Following along are instructions in the video below:
Right so for this problem. It says. Y equals.
Negative. X. Squared.
Plus. 6x minus minus 5. So by graphing it into vertex form.
We have to put it into form. Which is y equals. A times x.
Minus. H. Yes.
Do you need me to. Give. Something to somebody.
Ok. X. Minus.
H. Squared. Plus.
So we got to put into this format. So to be able to put into this format. What were going to do is were going to create a perfect square.
So by creating a perfect square. What im going to simply do is going to be what we say is completing the square. So remember you ladies and gentlemen to complete the square.
We cannot have anything as a except for one so here i have a negative one so the first thing. Im going to do is subtract out a negative one. Im sorry first thing.
Were going to do is im going to want to complete the square out of my first two terms. So lets just put parentheses around those first two terms all right then what we can do is realize that oh now we need to factor out a negative one. So lets factor out the negative one out of the first two terms.
Okay now what we can do is we can complete a square. So we factor out a negative 1. So therefore my a is going to be negative 1 alright.
So now we need to complete the square. So what were going to do again is just going to take your b divided by 2 and square it so negative 6 divided by 2 is negative 3 negative 3 squared is positive 9 so y equals negative 1 x. Squared minus 6x plus 9 minus.
9 minus. 5. All right.
But again later down. Here. Is where it comes a mistake that everybody comes up with remember i added a 9 right so i can add a 9 and subtract a 9 on the same side.
But since i added a 9 and that 9 is being multiplied by a negative 1 you have to multiply your negative 9 times a negative. 1 you guys just have to remember that step so now lets rewrite this as a perfect squared you meet you asked me how i got that one right.
And i said. The shortcut you can always just do x x plus b. Divided by 2 so b is negative.
6 divided by 2 which is a negative 3 right so you can just write this. Says. Y equals.
Negative 1 x. Minus 3. Squared plus 9.
Minus. 4. Is going to equal positive.
4. Does that make sense everything i did so far ok so now ladies and gentlemen. What were going to do is listen because we need to graph this right so we need to determine the vertex.
Remember. The vertex is h. Comma k.
3. Comma. 4.
All right and then lets determine is it going to open up or down well. Its going to open down right since my a is less than 0. Okay again light.
I like to do is i like to graph the parent graph. When graphing transformations so im going to graph the pantograph now parent graph has a vertex at 0 0.
It contains a point 1 1 and negative 1 1. Contains the point negative 2 4. And 2 comma.
4. All right. However thats what we call the paragraph thats with no transformations now what you guys can see is i have a transformation.
I have a new vertex right my vertex is now at 1 2. 3. 4.
All right thats my new vertex now. I know that the graph opens down right. So the graph is going to open down.
So now what we need to do is find our next two points well guys look at the relationship. The relationship between the points is over 1 up 1 over 2 up. 4.
Is there any change is there any vertical stretch or compression on this problem. No no so therefore your relationships can still going to be the same. Im going to go over 1 down.
1. Over 1 down. 1 over 2 down.
4. Over 2 down. 4 for from your vertex.
Okay. And then our blue is going to be our final answer. Anybody have any questions on that no good awesome yes sure .
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