Subjects

Algebra 2

Overview

How to Solve Quadratic Equations Step by Step

Name: Knowunity
Brand: Knowunity

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How to Solve Quadratic Equations Step by Step

lily

@lilyd.4

1 Follower

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

285

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:

x² + 8x = 2
x² + 8x + 16 = 18
(x + 4)² = 18
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

View

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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

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Subjects

Algebra 2

Overview

How to Solve Quadratic Equations Step by Step

lily

@lilyd.4

1 Follower

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

285

10th

Algebra 2

Page 2: Advanced Quadratic Concepts and Graphing

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:

x² + 8x = 2
x² + 8x + 16 = 18
(x + 4)² = 18
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

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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User