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How to Solve Quadratic Equations Step by Step

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lily

10/19/2023

Algebra 2

Solving and Graphing Quadratic Equations

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Algebra 2

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Overview

How to Solve Quadratic Equations Step by Step

La resolución de ecuaciones cuadráticas y el análisis de funciones cuadráticas son fundamentales en álgebra. Este material cubre cómo resolver ecuaciones cuadráticas paso a paso y explora diferentes métodos de solución.

  • Introduces the quadratic formula and its components (ax² + bx + c)
  • Explores multiple solving methods including factoring, completing the square, and the quadratic formula
  • Details the relationship between discriminant and number of solutions
  • Covers quadratic functions, their graphs, and vertex form
  • Explains axis of symmetry and its significance in graphing
...

10/19/2023

288

02: Solving quadratic equations Def: f(x) = AX²+BX+C A, B, C = TR O quadratic formula * solve = isolated vanable -> x==b+√√√b² - 4ac (** za

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Page 2: Advanced Quadratic Concepts and Graphing

This page delves deeper into solving quadratic equations and introduces práctica de factorización y gráfico de funciones cuadráticas. It explores different forms of quadratic functions and their graphical representations.

Definition: The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) represents the vertex.

Example: Converting x² + 8x - 2 = 0 to vertex form:

  1. x² + 8x = 2
  2. x² + 8x + 16 = 18
  3. (x + 4)² = 18
  4. x = -4 ± √18

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

The page concludes with practical graphing exercises, demonstrating how to find key points like y-intercepts and vertices.

Vocabulary:

  • Standard Form: f(x) = ax² + bx + c
  • Factored Form: f(x) = a(x - r₁)(x - r₂)
  • Vertex Form: f(x) = a(x - h)² + k

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Subjects

Algebra 2

Overview

Overview

 

Algebra 2

•

288

•

Oct 19, 2023

•

2 pages

How to Solve Quadratic Equations Step by Step

L

lily

@lilyd.4

La resolución de ecuaciones cuadráticas y el análisis de funciones cuadráticas son fundamentales en álgebra. Este material cubre cómo resolver ecuaciones cuadráticas paso a paso y explora diferentes métodos de solución.

  • Introduces the quadratic formula and its components (ax² +... Show more

02: Solving quadratic equations Def: f(x) = AX²+BX+C A, B, C = TR O quadratic formula * solve = isolated vanable -> x==b+√√√b² - 4ac (** za

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Page 2: Advanced Quadratic Concepts and Graphing

This page delves deeper into solving quadratic equations and introduces práctica de factorización y gráfico de funciones cuadráticas. It explores different forms of quadratic functions and their graphical representations.

Definition: The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) represents the vertex.

Example: Converting x² + 8x - 2 = 0 to vertex form:

  1. x² + 8x = 2
  2. x² + 8x + 16 = 18
  3. (x + 4)² = 18
  4. x = -4 ± √18

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

The page concludes with practical graphing exercises, demonstrating how to find key points like y-intercepts and vertices.

Vocabulary:

  • Standard Form: f(x) = ax² + bx + c
  • Factored Form: f(x) = a(x - r₁)(x - r₂)
  • Vertex Form: f(x) = a(x - h)² + k
02: Solving quadratic equations Def: f(x) = AX²+BX+C A, B, C = TR O quadratic formula * solve = isolated vanable -> x==b+√√√b² - 4ac (** za

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 1: Understanding Quadratic Equations and Solution Methods

This page introduces fundamental concepts of quadratic equations and various solving methods. The standard form of a quadratic equation is presented along with multiple solution techniques.

Definition: A quadratic equation is expressed as f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.

Highlight: The discriminant (b² - 4ac) determines the number of real solutions:

  • When D = 0: One real solution
  • When D > 0: Two real solutions
  • When D < 0: No real solutions

Example: Using the factoring method: x² + 8x - 15 = 0 (x + 3)(x + 5) = 0 x = -3 or x = -5

The page covers métodos para completar el cuadrado en ecuaciones cuadráticas and demonstrates how to convert expressions into perfect square trinomials.

Vocabulary: Perfect square trinomial - a quadratic expression that can be written as (x + p)².

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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 it’s very much worth it and you’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 don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’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 help🤍🤍

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.😋🩷🎀

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 😍😁😲🤑💗✨🎀😮

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 I’ve seen! Geometry too!

Paul T

iOS user