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How to Complete the Square and Find Turning Points in Quadratic Graphs

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narisse

26/02/2023

Maths

Completing the Square - GCSE Edexel Maths - Higher

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Algebraic expressions

How to Complete the Square and Find Turning Points in Quadratic Graphs

A comprehensive guide to completing the square method for quadratic equations and finding turning points in quadratic graphs.

  • The method involves transforming quadratic expressions into perfect square form
  • Key steps include factoring coefficients, grouping terms, and completing the square pattern
  • Understanding this technique helps locate the turning point in quadratic graphs
  • The process requires careful attention to signs and coefficients
  • Essential for analyzing quadratic functions and their graphical representations
...

26/02/2023

1791

Completing the square x² + 8x + 12 1 ½ 2 (x+4) ² → 2 (x+4) ²-4 Inverse sign ↓ -4 (x+4) (x+4) keep get to 1 12 = x² +8x + 16 Turning point (-

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Page 2: Advanced Completing the Square

This page explores more complex scenarios in factorising and completing the square in quadratics, particularly when dealing with coefficients other than 1. The example works through 2x² + 10x + 8.

Example: Converting 2x² + 10x + 8 into 2(x-2.5)² - 4.5

Highlight: When the x² coefficient isn't 1, factor it out before completing the square.

Definition: The turning point coordinates can be extracted from the completed square form, with x-coordinate being the negative of the number inside the brackets.

Completing the square x² + 8x + 12 1 ½ 2 (x+4) ² → 2 (x+4) ²-4 Inverse sign ↓ -4 (x+4) (x+4) keep get to 1 12 = x² +8x + 16 Turning point (-

View

Page 3: Practical Applications

This page applies the completing the square method to find the turning point of the quadratic function y = 2x² + 16x + 26, demonstrating practical applications in graphing.

Example: Converting 2x² + 16x + 26 into 2(x+4)² - 6

Highlight: The turning point (-4, -6) is essential for sketching the quadratic graph accurately.

Definition: The turning point represents the vertex of the parabola, where the function changes from increasing to decreasing or vice versa.

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Algebraic expressions

 

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3 pages

How to Complete the Square and Find Turning Points in Quadratic Graphs

user profile picture

narisse

@narisse

A comprehensive guide to completing the square method for quadratic equations and finding turning points in quadratic graphs.

  • The method involves transforming quadratic expressions into perfect square form
  • Key steps include factoring coefficients, grouping terms, and completing the square... Show more
Completing the square x² + 8x + 12 1 ½ 2 (x+4) ² → 2 (x+4) ²-4 Inverse sign ↓ -4 (x+4) (x+4) keep get to 1 12 = x² +8x + 16 Turning point (-

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Page 2: Advanced Completing the Square

This page explores more complex scenarios in factorising and completing the square in quadratics, particularly when dealing with coefficients other than 1. The example works through 2x² + 10x + 8.

Example: Converting 2x² + 10x + 8 into 2(x-2.5)² - 4.5

Highlight: When the x² coefficient isn't 1, factor it out before completing the square.

Definition: The turning point coordinates can be extracted from the completed square form, with x-coordinate being the negative of the number inside the brackets.

Completing the square x² + 8x + 12 1 ½ 2 (x+4) ² → 2 (x+4) ²-4 Inverse sign ↓ -4 (x+4) (x+4) keep get to 1 12 = x² +8x + 16 Turning point (-

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Page 3: Practical Applications

This page applies the completing the square method to find the turning point of the quadratic function y = 2x² + 16x + 26, demonstrating practical applications in graphing.

Example: Converting 2x² + 16x + 26 into 2(x+4)² - 6

Highlight: The turning point (-4, -6) is essential for sketching the quadratic graph accurately.

Definition: The turning point represents the vertex of the parabola, where the function changes from increasing to decreasing or vice versa.

Completing the square x² + 8x + 12 1 ½ 2 (x+4) ² → 2 (x+4) ²-4 Inverse sign ↓ -4 (x+4) (x+4) keep get to 1 12 = x² +8x + 16 Turning point (-

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Page 1: Basic Completing the Square

This page demonstrates the fundamental process of completing the square method for quadratic equations using a straightforward example with x² + 8x + 12. The method systematically transforms the quadratic expression into a perfect square form.

Example: Converting x² + 8x + 12 into (x+4)² - 4

Definition: Completing the square involves rewriting a quadratic expression in the form (x + p)² + q, where p and q are constants.

Highlight: The turning point can be directly read from the completed square form as (-4, -4).

Vocabulary: The term "perfect square" refers to an expression that can be written as a binomial squared.

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

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Best app on earth! no words because it’s too good

Thomas R

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Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

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Greenlight Bonnie

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very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

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I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

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Elisha

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This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

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