Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Finding the Vertex of a Parabola by Completing the Square  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Finding the vertex by completing the square; so what we have behind me is a parabola in standard form and I want to find the vertex of it and the only way I can do that is by completing the square.
So rules for completing the square are to isolate our xs together and to make sure that our coefficient on our x² term is 1. So what we have to do is isolate the xs from this 3 and there's two ways of doing that. We can either bring the 3 over to the other side, or just bring it outside of our parenthesis. I'm going to do the latter, I'm just going to bring it to the outside, but if you want to bring it around, you can do that as well.
The other thing we have to do is get the coefficient on our x² to be a 1, so what I have to do is then factor out a 2 from everything that has an x. Let's go ahead and do that one.
So what we end up with is f(x) stays the same and we end up with 2, x² and we're taking a 2 out of 8 so this turns to 4x and my +3 I just brought that side of the parenthesis.
So we now what to complete the square, so we want to figure out what goes in here to make this a perfect square, divide the middle term by 2, 4 divide by 2 is 2, and square that so we are adding 4 inside of our parenthesis.
Now be careful, we're adding 4 inside of the parenthesis, but what we're actually doing is that plus 4 is getting multiplied by 2, so we've actually subtracted 8 by putting that 4 in here, subtracted 8 from that part, so in order to keep it balanced, I have to add 8 outside the parenthesis. So we add 8 out here, so what we actually end up with is +11 on the outside and we have f(x) equals.
I was able to find my vertex, my vertex is going to be (2,11). The graph is going to be shifted up 11 to the right 2 and this 2 is going to tell me that my graph is going to be a little bit steeper and actually flipped upside down because of that negative.
So finding the vertex of an equation by completing the square; always make sure you have your x² coefficient to be 1 and make sure that when you add or subtract something inside the parenthesis you have to distribute whatever you factored out.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Sample Problems (8)
Need help with a problem?
Watch expert teachers solve similar problems.

Finding the Vertex of a Parabola by Completing the Square
Problem 1 7,237 viewsFind the vertex of:
y = x² − 4x + 6 
Finding the Vertex of a Parabola by Completing the Square
Problem 2 5,304 viewsFind the vertex of:
f(x) = 2x² + 8x + 3 
Finding the Vertex of a Parabola by Completing the Square
Problem 3 4,242 viewsFind the vertex of:
f(x) = ½x² + 3x + 4 
Finding the Vertex of a Parabola by Completing the Square
Problem 4 414 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 5 416 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 6 322 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 7 398 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 8 428 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete