Mastering Completing the Square: A Step-by-Step Guide from Khan Academy

Are you struggling with completing the square? Does the thought of solving quadratic equations make you break into a sweat? Don't worry, because Khan Academy has got your back!

Khan Academy is an online platform that provides free educational resources to students all around the world. Their math courses are particularly popular and have helped countless students ace their exams. Completing the square is one of the many topics covered in their Algebra II course.

So, what exactly is completing the square? Essentially, it's a technique used to rewrite a quadratic equation in a more useful form. This technique can be especially helpful when you're trying to solve a quadratic equation by factoring. But how do you actually complete the square?

Firstly, it's important to understand the basic structure of a quadratic equation: y = ax^2 + bx + c. The goal of completing the square is to turn the right-hand side of the equation (ax^2 + bx) into a perfect square trinomial. This is done by adding and subtracting a specific value, which depends on the values of a and b.

Okay, so that's the theory, but how do you actually apply this technique in practice? Well, luckily, Khan Academy has a fantastic video tutorial that walks you through the steps of completing the square. The video is clear and concise, with plenty of examples to help you understand the concept.

In addition to the video tutorial, Khan Academy also provides practice problems for you to work on. These problems start off easy and gradually get harder, so you can build your skills at your own pace. The problems also come with step-by-step solutions, so you can see where you went wrong if you make a mistake.

But what about if you're still struggling with completing the square, even after watching the video and doing the problems? Well, don't despair - Khan Academy has a fantastic community forum where you can ask for help. The forum is moderated by experienced tutors and fellow students, so you can be sure that you'll get accurate and helpful responses.

So, to sum up: completing the square doesn't have to be a daunting task. With the help of Khan Academy, you can master this technique and ace those quadratic equations. Plus, since Khan Academy is completely free, you don't even have to spend a penny to access their excellent resources. So why not give it a go?

If you're still not convinced, consider this: studies have shown that students who use Khan Academy regularly perform better in exams than those who don't. Plus, Khan Academy has been endorsed by big names such as Bill Gates and Salman Khan (the founder). So what are you waiting for? Check out Khan Academy's Algebra II course and start completing those squares!

Ultimately, completing the square is an essential skill for any student of algebra. By mastering this technique, you'll not only be able to solve quadratic equations with ease, but you'll also have a deeper understanding of algebraic concepts. So why not take advantage of Khan Academy's fantastic resources and become an algebra superstar?

"How To Complete The Square Khan Academy" ~ bbaz

Introduction

Completing the square is a fundamental part of algebra that many students find challenging. However, with its ability to simplify quadratic expressions and solve complex equations, completing the square is an essential skill to master for any student of algebra.

What is Completing the Square?

Completing the square is a process used in algebra to convert a quadratic equation from standard form (ax^2 + bx + c) to vertex form (a(x - h)^2 + k), where (h,k) represents the vertex of the parabola.

Why is it important to Complete the Square?

Completing the square is an essential skill to master because it allows you to identify the vertex of a parabola, which can be used to model many real-world problems. It also simplifies the process of solving quadratic equations, making it easier to find the roots (x-intercepts) of a parabola.

The Steps to Completing the Square

To complete the square, you must follow these steps:

1. Move the constant term to the other side of the equation.
2. Divide the coefficient of x² by 2.
3. Square the result obtained in step 2.
4. Add and subtract this result to the equation.
5. Simplify the equation by factoring the trinomial as a perfect square.

An Example on How to Complete the Square Using Khan Academy

Let's take the example of the equation:

x^2 + 6x + 4 = 0

Step 1: Move the constant term to the other side of the equation:

x^2 + 6x = -4

Step 2: Divide the coefficient of x² by 2:

a = 1, b = 6, c = -4

b/2a = 6/2(1) = 3

Step 3: Square the result obtained in step 2:

(3)^2 = 9

Step 4: Add and subtract this result to the equation:

x^2 + 6x + 9 - 9 = -4

Step 5: Simplify the equation by factoring the trinomial as a perfect square:

(x + 3)^2 - 13 = 0

Conclusion

Completing the square is an important skill to master in algebra. It simplifies the process of solving quadratic equations and allows you to identify the vertex of a parabola. Following the steps outlined above will help you complete the square with ease. With practice and understanding, you can use this technique to solve complex algebraic problems with confidence.

How To Complete The Square: Khan Academy

Introduction

Completing the square is a fundamental concept in algebra. It is often used to solve quadratic equations, graph parabolas, and find the vertex of a quadratic function. Khan Academy is one of the most popular online resources for learning how to complete the square. In this comparison blog article, I will explore Khan Academy's approach to completing the square and compare it with other resources.

Khan Academy's Explanation of Completing the Square

Khan Academy breaks down completing the square into four simple steps, starting with isolating the constant term on one side of the equation. The second step involves dividing the coefficient of the x-term by two and then squaring the result. The third step is adding this result to both sides of the equation, and finally, the fourth step is simplifying the equation by factoring the perfect square trinomial.

Step 1: Isolate the Constant Term

To isolate the constant term, you must move all the terms to one side of the equation. Let's take the example equation 'x^2+6x+8=0.' If we subtract 8 from both sides of the equation, we are left with 'x^2+6x=-8.'

Step 2: Divide by Two and then Square the Result

After isolating the constant term, we use the coefficient of the x-term to complete the square. We start by dividing it by two and then squaring the result. Continuing with the same example, since the coefficient of the x-term is six, half of it is three, and three squared is nine.

Step 3: Add the Result to Both Sides of the Equation

After finding the perfect square, we add it to both sides of the equation. In this example, we add nine to both sides, giving us 'x^2+6x+9=-8+9.'

Step 4: Factor the Perfect Square Trinomial

The final step of completing the square is to factor the resulting perfect square trinomial. By doing this, we get '(x+3)^2=1.' Then, by taking the square root of both sides, we get 'x=-3±√1.'

Completing the Square: Khan Academy vs Other Resources

Completing the square is a difficult concept for many students to master, and they often need to use multiple resources to understand it fully. I have compared Khan Academy's approach to other online resources, such as Mathway and Purplemath. I found that Khan Academy's approach was the most comprehensive and user-friendly.

Explanation of the Steps

Khan Academy gives an in-depth explanation of each step of completing the square, making it easy for students to follow along. Mathway and Purplemath also cover the basic steps, but their explanations are not as detailed.

Examples and Practice Problems

Khan Academy offers several examples and practice problems to help students understand and apply the concept of completing the square. Mathway and Purplemath also offer practice problems, but Khan Academy provides more variety and feedback.

Accessibility and Affordability

Khan Academy is a free and accessible resource that can be used on multiple platforms, including desktop computers, tablets, and smartphones. In contrast, Mathway and Purplemath require a paid subscription to access all the features.

Conclusion

Overall, Khan Academy's approach to completing the square is an excellent resource for students who struggle with this concept. The four-step method is easy to follow and understand, and the examples and practice problems make it easy for students to apply their knowledge. Compared to other resources, Khan Academy offers a more comprehensive and user-friendly learning experience.

How To Complete The Square Khan Academy

Introduction

Completing the square is a technique that can be used to solve quadratic equations. It involves manipulating an equation into a form that can easily be solved by factoring or using the quadratic formula. Completing the square can be a bit tricky, so in this article, we will go over the steps for completing the square using Khan Academy.

Step 1: Rewrite the Quadratic Equation

The first step in completing the square is to rewrite the quadratic equation in the form of (x + a)² + b = c. This means that we need to find a value a and b that can be added or subtracted from the quadratic equation to get this new form.

Example:

Consider the quadratic equation: x² + 6x + 4 = 0. To rewrite this equation in the (x + a)² + b = c form, we need to find values for a and b such that: x² + 6x + 4 = (x + a)² + b.

Step 2: Find ‘a’ Value

To find the value of a, divide the coefficient of x by 2 and square the result. We add this value to both sides of the equation.

Example:

For our example, the coefficient of x is 6. Dividing by 2, we get 3. Squaring this value gives us 9. Therefore, we add 9 to both sides as follows:x² + 6x + 9 + 4 - 9 = (x + 3)² - 5 = 0

Step 3: Simplify the Equation

We can now simplify the equation by combining like terms.

Example:

Using the example above, we can combine 9 and 4 to get 13. Therefore, our equation becomes:(x + 3)² - 5 = 0

Step 4: Solve for x

To solve for x, we move the constant term, -5, to the other side of the equation and take the square root of both sides.

Example:

Continuing with our example above, if we add 5 to both sides we get:(x + 3)² = 5Taking the square root of both sides gives us:x + 3 = ±√5Therefore, x can be solved as follows:x = -3 ±√5

Conclusion

Completing the square can be a bit challenging, especially if you are not familiar with the quadratic equation. However, by following the steps outlined above, you should be able to get a good understanding of how to complete the square using Khan Academy. Just remember to practice completing the square with different quadratic equations to help you become more comfortable with the process. With enough practice, you’ll be able to solve even the most complicated quadratic equations in no time!

How To Complete The Square Khan Academy: A Comprehensive Guide

Completing the square is a fundamental concept in Algebra, used to solve quadratic equations and graph parabolas. It involves manipulating an equation until it is in a format where it can be factored easily. In this blog post, we will guide you through How To Complete The Square Khan Academy, a popular online learning platform that offers free interactive math lessons.

If you are looking for a step-by-step guide on how to complete the square Khan Academy, then you've come to the right place! Before we delve into the details, let's first understand what completing the square means. At its core, completing the square involves finding a constant value that, when added or subtracted from an expression, creates a perfect square trinomial.

The process of completing the square Khan Academy can be overwhelming at first, especially if you are new to algebraic concepts. However, with some practice and patience, you will quickly get the hang of it. The main goal of completing the square is to rewrite quadratic expressions in a simplified form that allows you to solve for x.

The first step towards completing the square Khan Academy is to make sure that the quadratic expression is in standard form, which resembles y = ax^2 + bx + c. If the quadratic equation is not in standard form, you will need to move all the constants and coefficients to one side to get it into the correct format.

Once you have your quadratic expression in standard form, the next step in completing the square Khan Academy is to determine the value of a and b. a represents the coefficient of the squared term, while b represents the coefficient of the linear term. These values will be used to find the midpoint of the x-axis and the vertex of the parabola.

After finding the values of a and b, you will need to find the value of c by moving all the constants to the right-hand side of the equation. At this point, you can then add or subtract from both sides of the equation to create a perfect square trinomial.

The process of completing the square Khan Academy can be explained using a practical example. Let's say we have the expression y = x^2 + 8x + 12. To complete the square, you would start by identifying a and b. In this case, a = 1 and b = 8.

You would then calculate the midpoint of the x-axis by taking half of the linear coefficient and squaring it. Next, you would add this value to both sides of the equation to create a perfect square trinomial. in this case, the value is 16, and your equation would become y = (x + 4)^2 - 4.

Once you have your equation in the perfect square trinomial format, you can easily solve for x by taking the square root of both sides. Then, take the positive and negative square roots and plug them into your equation to get two possible solutions.

In conclusion, completing the square Khan Academy is an essential skill for both Algebra I and II learners. By breaking down the concepts into simple steps, Khan Academy makes it easy for students to master this skill. Learning how to complete the square with Khan Academy will give you the tools you need to solve quadratic equations and graph parabolas correctly. With this guide, you now have the knowledge and confidence you need to tackle completing the square problems with ease!

We hope this guide has been helpful to you in understanding how to complete the square Khan Academy. If you have any questions or feedback, please leave a comment below.

Thank you for reading this comprehensive guide to How To Complete The Square Khan Academy.

How To Complete The Square Khan Academy

What is completing the square?

Completing the square is a method used in algebra to rewrite quadratic equations into a standard form that allows easier factoring or solving for roots. By adding or subtracting a constant to the quadratic equation, one can create a perfect square trinomial, which can then be factored using simple algebra.

Why do we need to complete the square?

Completing the square is helpful in various algebraic applications, such as finding the minimum and maximum values of a quadratic function, graphing quadratic equations, and solving problems involving projectile motion. Completing the square is also a crucial step in deriving the quadratic formula, which is one of the most fundamental formulas in mathematics.

What is the process of completing the square?

Here are the step-by-step instructions for completing the square:

1. Write the quadratic equation in the standard form: ax² + bx + c = 0
2. Divide both sides of the equation by a (the coefficient of the x² term)
3. Subtract c/a from both sides
4. Add (b/2a)² to both sides of the equation
5. Simplify the right side of the equation to a perfect square trinomial
6. Factor the perfect square trinomial on the right side of the equation
7. Add or subtract the constant on the left side of the equation to solve for x

How can I practice completing the square?

Khan Academy offers an excellent resource for practicing completing the square through online video tutorials and interactive exercises. Simply go to khanacademy.org and search for Completing the Square.

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