Summary Quick Guide to Completing the Square (Youtube) youtu.be
1,111 words - YouTube video - View YouTube video
One Line
The video showcases two effective methods for completing the square, a useful technique for equation transformation and problem-solving.
Slides
Slide Presentation (6 slides)
Key Points
- Completing the square is a useful technique for writing equations in vertex form and solving them.
- The goal of completing the square is to create a perfect square trinomial, which can be factored down into a binomial squared.
- To create a perfect square trinomial, you need to determine the number that, when added to the equation, will complete the square.
- When completing the square, it is important to add and subtract the same number on both sides of the equation to maintain equivalence.
- Another method for completing the square is to put parentheses around the first two terms of the equation and then calculate (b/2)^2 to find the value that creates the perfect square trinomial.
- Adding and subtracting the calculated value on the same side of the equation can simplify the process of completing the square.
- By completing the square, an equation can be written in vertex form, making it easier to solve.
- A step-by-step method for completing the square will be explained in the next video.
Summaries
17 word summary
This video demonstrates two methods for completing the square, which is useful for transforming equations and problem-solving.
70 word summary
This video is a quick guide to completing the square for various purposes such as writing equations in vertex form, identifying the vertex of a parabola, and solving equations. Two methods are demonstrated: adding a number to create a binomial squared, and adding/subtracting the squared value of half the x term coefficient. Recognizing the perfect square trinomial value is emphasized. Completing the square is useful for transforming equations and problem-solving.
158 word summary
This video provides a quick guide to completing the square, which is useful for various purposes such as writing equations in vertex form, identifying the vertex of a parabola, and solving equations. The goal of completing the square is to create a perfect square trinomial. The speaker demonstrates two methods for completing the square. The first method involves identifying the number needed to create the binomial squared by adding it to both sides of the equation. The second method involves dividing the coefficient of the x term by 2, squaring it, and adding/subtracting that value on the same side of the equation. After creating the perfect square trinomial, it can be factored down. The speaker emphasizes the importance of recognizing the value that creates the perfect square trinomial, which can be determined by dividing the coefficient of the x term by 2 and squaring it. Completing the square is a useful technique for transforming equations and solving problems.
404 word summary
In this video, the speaker provides a quick guide to completing the square. Completing the square can be useful for writing an equation in vertex form, identifying the vertex of a parabola, and solving equations. The main goal of completing the square is to create a perfect square trinomial.
To illustrate the process, the speaker changes the equation to a simpler one to demonstrate the basic idea. A perfect square trinomial is a trinomial where the first term and the last term are both squared. This type of trinomial can be factored into a binomial squared, which is the desired result when completing the square.
There are two methods presented for completing the square. The first method involves identifying the number needed to create the binomial squared. In the example given, the speaker already has an x squared term and a 6x term, so they just need to add 9 to complete the square. It is important to remember to add the same number to both sides of the equation.
The second method involves recognizing that the first two terms of the equation are what need to be turned into a perfect square. To find the value needed, divide the coefficient of the x term by 2 and square it. In this case, 6 divided by 2 squared equals 9. Instead of adding 9 to one side and subtracting 9 from the other side, the speaker suggests adding and subtracting 9 on the same side to simplify the process.
After creating the perfect square trinomial, it can be factored down. In this example, it factors into (x + 3) squared. To solve for y, subtract 9 from both sides of the equation.
The speaker emphasizes that completing the square can be more challenging when it is not immediately obvious what value creates the perfect square trinomial. However, by dividing the coefficient of the x term by 2 and squaring it, the value can be determined. In this case, 6 divided by 2 squared equals 9. Subtracting 9 from both sides of the equation and adding and subtracting it on the same side simplifies the process.
Overall, completing the square is a useful technique for transforming equations into vertex form, identifying the vertex of a parabola, and solving equations. The two methods presented in the video provide different approaches to completing the square, depending on whether the perfect square trinomial is immediately recognizable or not.
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Source: https://youtu.be/MveZ6dyKMuA?si=d3PXopxYND1RSaFG
Page title: Quick Guide to Completing the Square - YouTube
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