what is the vertex of g(x) = –3×2 + 18x + 2? 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 Learn how to find the vertex of a parabola. Following along are instructions in the video below:
Right cool stuff and we got sound were all good but we got tangled tangled cord all right so what i have here ladies and gentleman is f of equals. Negative. X.
Squared. Plus. 2x plus.
5. All right all right okay. So remember.
The first step. We always want to do is make sure its in our quadratic form. Which are the definition of our quadratic.
Which is ax squared. Plus. Bx plus c.
Right. So. This is an f form.
Were good the next thing. We want to do is make sure our a is going to be 1 here we have a as a negative 1. So i have to factor that out when i factor that out if i have my squared and my linear term.
I want to factor it out of both of those terms. Im i prefer just to factor out of these two terms all right so when i factor that out im now left with a negative 1 or do you can just do the negative right negative. Now i have x squared minus.
2x plus. 5. Okay now the way ill explain it this before so.
Now. All i do is i factored a negative 1 out of those first two terms alright. So what were going to do is for this binomial.
We are going to create a perfect square trinomial does anybody recognize perfect square trinomial lets just go through it again right because i think its important if you guys understand what perfect square. Trinomials are ill just give you guys two good examples x. Squared.
Plus. 10x plus. 25.
All right these are two perfect square. Trinomials. Why theyre perfect square trinomials.
Well. If you practice factory. Now.
This comes. In 2 x. Plus.
5. Times. X.
Plus. 5. Right.
5. Times. 5.
Is. 25. 5.
Plus. 5. Is.
10. This. One is x plus.
2. Times. X.
Plus. 2. Right well.
What you notice is this is the same thing multiplied by itself. So we can just rewrite. It as x plus.
2. Squared. X.
Plus. 5. Squared.
Thats why. Its so important to have a perfect square trinomial because we can rewrite it we can factor. It as x plus.
5. Squared or we can write read as a binomial squared got it okay. So thats why we want to get a perfect square trinomial.
So now once we first have it in quadratic form. Then we factor out so we have a 1 as our a now i need to make this binomial create this to be a perfect square trinomial. So im going to create a perfect square trinomial.
So rather than always thinking you know what how would it be theres a very easy process and that process is to take negative. 2 divided by b take b divided by 2 and square it so for this problem our b is negative 2 negative 2 divided by 2 squared negative 2 divided by 2 is negative 1 negative 1 squared is 1 right so what i do is rewrite it now x. Squared.
Minus. 2x plus. 1.
I have now created a perfect square. Trinomial. That is a perfect square trinomial.
Okay. Thats what the b over 2 squared did to me that created that perfect square trinomial. But remember if im going to add 1.
This is this is a problem so if i add 1 now im going to subtract 1. And then plus 5. But heres again we need to remember heres where a lot of mistakes came in since im multiplying this positive 1 by negative 1.
Thats really a negative 1. So i need to make sure i multiply by this negative sign to this negative. 1 so im multiplying negative.
1. Again therefore now i can rewrite this member perks for trinomials. We can rewrite as a binomial squared.
So equals negative x. Minus. 1.
Squared negative. 1 times negative. 1.
Is positive 1 plus. 5 is 6. Yes well the thing thats why i fact thats why i just its different ways to solve it thats why i prefer just to solve with here.
So you dont have to deal with that because thats your k. And you can just leave it leave it there so then whats up so then what you have is now its in vertex form. Which our vertex form is f of.
X. Equals. A.
Times x minus. H. Squared.
Plus. K. Where.
Your vertex is equal to h. Comma. K.
Notice. That the vertex is the opposite sign here so my vertex. Which you should have got is going to equal 1 comma.
6 right its the opposite sign of whats in your standard form if its x minus h. Its going to be h. Got it cool.
Then the next step is to solve so to solve were going to make sure we have f of x. Which is our output. Were going to set equal to 0.
So i have negative x minus. 1. Squared plus 6.
And subtract the 6 on both sides so i get negative. 6. Equals.
Negative x minus 1. Squared. Then i got to get rid of the negative 1.
So i divide by negative 1 on both sides and i get positive. 6. Equals.
X minus 1 squared now i undo the squaring function. So i square root. And i get square root of 6 equals.
X. Minus. 1.
The other mistake. A lot of students made is to remember. That when you have a square root of 6 equals.
X. Minus. 1.
Make sure that you take in the plus. And minus of the square root of 6. So my final answer is going to be x equals.
I add the 1 to the other side 1 plus or minus square root of 6 thats your final answer x intercepts vertex ok perfect timing. .
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