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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,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 f(x) = 3xยฒ - 6x + 5:

  • Vertex calculation: h = -(-6)/(2(3)) = 1
  • k = f(1) = 2
  • Therefore, vertex is (1,2)
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 f(x) = 3xยฒ - 6x + 5:

  • Vertex: V(1,2)
  • Axis of symmetry: x = 1
  • y-intercept: (0,5)
  • 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 (x-intercepts) and provides additional practice with vertex calculations.

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

Example: For f(x) = xยฒ - 4x + 3:

  • x-intercepts: (1,0) and (3,0)
  • y-intercept: (0,3)
  • Vertex: (2,-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

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

user profile picture

Stephanie๐Ÿ’œ

@stephanie_071607

ยท

602 Followers

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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

ย 

9th/10th

ย 

Algebra 1

6

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,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 f(x) = 3xยฒ - 6x + 5:

  • Vertex calculation: h = -(-6)/(2(3)) = 1
  • k = f(1) = 2
  • Therefore, vertex is (1,2)
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 content. It'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 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 f(x) = 3xยฒ - 6x + 5:

  • Vertex: V(1,2)
  • Axis of symmetry: x = 1
  • y-intercept: (0,5)
  • 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

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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 (x-intercepts) and provides additional practice with vertex calculations.

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

Example: For f(x) = xยฒ - 4x + 3:

  • x-intercepts: (1,0) and (3,0)
  • y-intercept: (0,3)
  • Vertex: (2,-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 content. It's free!

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Join milions of students

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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 f(x) = axยฒ + bx + c, where a, b, and c are constants and a โ‰  0.

Example: For the function f(x) = 3xยฒ - bx + 5:

  • a = 3
  • b = -b
  • c = 5

Highlight: Function evaluation is demonstrated through calculating f(0) = 5, f(1) = 2, and f(-1) = 14.

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.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

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

4.9+

Average App Rating

20 M

Students use Knowunity

#1

In Education App Charts in 17 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 โค๏ธ, I use it basically all the time whenever I'm studying