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Easy Steps to Find the Vertex and Axis of Symmetry in Quadratic Equations

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Stephanie๐Ÿ’œ

12/21/2023

Algebra 1

Quadratic Functions in Standard Form

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Algebra 1

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Quadratics

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Intro to Parabolas

Easy Steps to Find the Vertex and Axis of Symmetry in Quadratic Equations

A comprehensive guide to understanding axis of symmetry in quadratic equations and finding key points of quadratic functions in standard form.

  • Learn to identify components of quadratic functions including a, b, and c values
  • Master techniques for how to find the vertex of a quadratic function using the formula h = -b/2a
  • Understand how to calculate y-intercept in standard form quadratic equation and determine x-intercepts
  • Explore domain, range, and graphical representations of quadratic functions
  • Practice with real-world examples and step-by-step solutions
...

12/21/2023

144

D 8 Warm-Up 1. The standard form of a quadratic function is f(x) = ax 2 +bx+c Identify the values of a, b, and C in: f(x) = 3xยฒ-bx+5 a = 3 b

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Page 2: Finding Key Points of Quadratic Functions

This page details the process of finding important points and characteristics of quadratic functions, particularly focusing on the vertex and y-intercept.

Vocabulary: The vertex h,kh,k represents the highest or lowest point of a quadratic function.

Definition: The axis of symmetry is a vertical line that passes through the vertex, given by x = -b/2a.

Example: For fxx = 3xยฒ - 6x + 5:

  • Vertex calculation: h = -โˆ’6-6/2(32(3) = 1
  • k = f11 = 2
  • Therefore, vertex is 1,21,2
D 8 Warm-Up 1. The standard form of a quadratic function is f(x) = ax 2 +bx+c Identify the values of a, b, and C in: f(x) = 3xยฒ-bx+5 a = 3 b

View

Page 3: Graphical Analysis of Quadratic Functions

This page explores the graphical representation of quadratic functions and their key characteristics.

Highlight: The domain of a quadratic function includes all real numbers, while the range depends on whether the parabola opens up or down.

Example: For fxx = 3xยฒ - 6x + 5:

  • Vertex: V1,21,2
  • Axis of symmetry: x = 1
  • y-intercept: 0,50,5
  • Range: [2,โˆž)
D 8 Warm-Up 1. The standard form of a quadratic function is f(x) = ax 2 +bx+c Identify the values of a, b, and C in: f(x) = 3xยฒ-bx+5 a = 3 b

View

Page 4: Zeros and Additional Features

This page covers the concept of zeros xโˆ’interceptsx-intercepts and provides additional practice with vertex calculations.

Definition: A zero of a function is an x-value that makes fxx = 0, also known as an x-intercept.

Example: For fxx = xยฒ - 4x + 3:

  • x-intercepts: 1,01,0 and 3,03,0
  • y-intercept: 0,30,3
  • Vertex: 2,โˆ’12,-1

Highlight: The vertex formula h = -b/2a is consistently used throughout different examples to find the turning point of quadratic functions.

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Subjects

Algebra 1

Quadratics

Intro to Parabolas

ย 

Algebra 1

โ€ข

144

โ€ข

Dec 21, 2023

โ€ข

4 pages

Easy Steps to Find the Vertex and Axis of Symmetry in Quadratic Equations

user profile picture

Stephanie๐Ÿ’œ

@stephanie_071607

A comprehensive guide to understanding axis of symmetry in quadratic equations and finding key points of quadratic functions in standard form.

  • Learn to identify components of quadratic functions including a, b, and c values
  • Master techniques for how to find... Show more

D 8 Warm-Up 1. The standard form of a quadratic function is f(x) = ax 2 +bx+c Identify the values of a, b, and C in: f(x) = 3xยฒ-bx+5 a = 3 b

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Page 2: Finding Key Points of Quadratic Functions

This page details the process of finding important points and characteristics of quadratic functions, particularly focusing on the vertex and y-intercept.

Vocabulary: The vertex h,kh,k represents the highest or lowest point of a quadratic function.

Definition: The axis of symmetry is a vertical line that passes through the vertex, given by x = -b/2a.

Example: For fxx = 3xยฒ - 6x + 5:

  • Vertex calculation: h = -โˆ’6-6/2(32(3) = 1
  • k = f11 = 2
  • Therefore, vertex is 1,21,2
D 8 Warm-Up 1. The standard form of a quadratic function is f(x) = ax 2 +bx+c Identify the values of a, b, and C in: f(x) = 3xยฒ-bx+5 a = 3 b

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

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Page 3: Graphical Analysis of Quadratic Functions

This page explores the graphical representation of quadratic functions and their key characteristics.

Highlight: The domain of a quadratic function includes all real numbers, while the range depends on whether the parabola opens up or down.

Example: For fxx = 3xยฒ - 6x + 5:

  • Vertex: V1,21,2
  • Axis of symmetry: x = 1
  • y-intercept: 0,50,5
  • Range: [2,โˆž)
D 8 Warm-Up 1. The standard form of a quadratic function is f(x) = ax 2 +bx+c Identify the values of a, b, and C in: f(x) = 3xยฒ-bx+5 a = 3 b

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Zeros and Additional Features

This page covers the concept of zeros xโˆ’interceptsx-intercepts and provides additional practice with vertex calculations.

Definition: A zero of a function is an x-value that makes fxx = 0, also known as an x-intercept.

Example: For fxx = xยฒ - 4x + 3:

  • x-intercepts: 1,01,0 and 3,03,0
  • y-intercept: 0,30,3
  • Vertex: 2,โˆ’12,-1

Highlight: The vertex formula h = -b/2a is consistently used throughout different examples to find the turning point of quadratic functions.

D 8 Warm-Up 1. The standard form of a quadratic function is f(x) = ax 2 +bx+c Identify the values of a, b, and C in: f(x) = 3xยฒ-bx+5 a = 3 b

Sign up to see the contentIt's free!

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Introduction to Quadratic Functions

This page introduces the fundamental concepts of quadratic functions in standard form. The content focuses on identifying key components and evaluating functions at specific points.

Definition: A quadratic function in standard form is written as fxx = axยฒ + bx + c, where a, b, and c are constants and a โ‰  0.

Example: For the function fxx = 3xยฒ - bx + 5:

  • a = 3
  • b = -b
  • c = 5

Highlight: Function evaluation is demonstrated through calculating f00 = 5, f11 = 2, and fโˆ’1-1 = 14.

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Paul T

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

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.

Samantha Klich

Android user

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

iOS user

I think itโ€™s very much worth it and youโ€™ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still donโ€™t get it!!! In the end I think itโ€™s worth it ๐Ÿ˜Š๐Ÿ‘ โš ๏ธAlso DID I MENTION ITS FREEE YOU DONโ€™T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLYโ—๏ธโ—๏ธโš ๏ธ

Thomas R

iOS user

Knowunity is the BEST app Iโ€™ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help๐Ÿค๐Ÿค

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.๐Ÿ˜‹๐Ÿฉท๐ŸŽ€

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐Ÿ˜๐Ÿ˜๐Ÿ˜ฒ๐Ÿค‘๐Ÿ’—โœจ๐ŸŽ€๐Ÿ˜ฎ

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as Iโ€™ve seen! Geometry too!

Paul T

iOS user