Subjects

Algebra 1

Quadratics

Vertex Form

449

•

Apr 18, 2023

•

4 pages

Easy Steps to Convert Standard Form to Vertex Form - Vertex Form Calculator Included

Name: Knowunity
Brand: Knowunity

Olivia ingalls

@oliviaingalls_okwr

Quadratic equations and their graphing are essential topics in algebra.... Show more

Name:
Topic:
Main Ideas/Questions
Steps to Graph a
QUADRATIC
EQUATION
EXAMPLES
X=-b
га
Notes/Examples
Find the axis of symmetry.
Axis of Sym

Vertex Form of Quadratic Equations

This page focuses on the vertex form of quadratic equations and how to interpret it.

The vertex form of a quadratic equation is y = a $x - h$ ² + k, where $h, k$ represents the vertex of the parabola. This form is particularly useful for identifying the axis of symmetry and vertex directly from the equation.

The page provides practice problems for identifying the axis of symmetry and vertex from equations in vertex form. It also includes examples of graphing quadratic functions in vertex form.

Definition: The vertex form of a quadratic equation is y = a $x - h$ ² + k, where $h, k$ is the vertex of the parabola.

Example: For y = - $x - 3$ ², the axis of symmetry is x = 3, and the vertex is $3, 0$ .

Highlight: The vertex form is particularly useful for quickly identifying the key features of a quadratic function, such as its vertex and axis of symmetry.

Transformations from the Parent Function

This page explores transformations of quadratic functions from the parent function y = x².

Transformations can include:

Vertical and horizontal shifts
Reflections
Vertical stretches or compressions

The page provides examples of graphing transformed quadratic functions and describing how they compare to the parent function.

Vocabulary: A transformation is a change to the size, shape, or position of a figure.

Example: The function y = $x + 2$ ² represents a shift of the parent function 2 units to the left.

Highlight: Understanding transformations is crucial for quickly sketching quadratic functions and predicting their behavior based on their equation.

Writing Equations and Putting It All Together

This final page combines all the concepts learned to write equations based on described transformations.

Key points about the vertex form y = a $x - h$ ² + k:

h represents the horizontal shift $positive h shifts left, negative h shifts right$
k represents the vertical shift $positive k shifts up, negative k shifts down$
If a is negative, the function is reflected over the x-axis
|a| > 1 represents a vertical stretch, while 0 < |a| < 1 represents a vertical compression

The page includes practice problems for writing equations based on described transformations from the parent function.

Example: A function translated 3 units left and 4 units down can be represented as y = $x + 3$ ² - 4.

Highlight: Being able to write equations based on described transformations demonstrates a deep understanding of how the coefficients and constants in a quadratic equation affect its graph.

Vocabulary: Vertical stretch occurs when |a| > 1, while vertical compression occurs when 0 < |a| < 1 in the vertex form of a quadratic equation.

Graphing Quadratic Equations

This page introduces the steps to graph a quadratic equation and provides examples for practice.

To graph a quadratic equation:

Find the axis of symmetry using the formula x = -b/ $2a$
Calculate the vertex
Create a table of values
Plot points and connect them into a smooth parabola

The page includes practice problems for graphing quadratic equations and identifying key features such as the axis of symmetry, vertex, domain, and range.

Example: For y = x² + 2x - 1, the axis of symmetry is x = -1, and the vertex is $-1, -2$ .

Vocabulary: Domain refers to all possible x-values, while range refers to all possible y-values of the function.

Highlight: Understanding how to graph quadratic equations is crucial for visualizing their behavior and identifying important characteristics.

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Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user

Subjects

Algebra 1

Quadratics

Vertex Form

Algebra 1

•

449

•

Apr 18, 2023

•

4 pages

Easy Steps to Convert Standard Form to Vertex Form - Vertex Form Calculator Included

Olivia ingalls

@oliviaingalls_okwr

Quadratic equations and their graphing are essential topics in algebra. This guide covers standard form to vertex form conversion, graphing quadratic functions, and understanding transformations of quadratic functions. It provides step-by-step instructions, examples, and practice problems to help students master... Show more

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Vertex Form of Quadratic Equations

This page focuses on the vertex form of quadratic equations and how to interpret it.

The page provides practice problems for identifying the axis of symmetry and vertex from equations in vertex form. It also includes examples of graphing quadratic functions in vertex form.

Definition: The vertex form of a quadratic equation is y = a $x - h$ ² + k, where $h, k$ is the vertex of the parabola.

Example: For y = - $x - 3$ ², the axis of symmetry is x = 3, and the vertex is $3, 0$ .

Highlight: The vertex form is particularly useful for quickly identifying the key features of a quadratic function, such as its vertex and axis of symmetry.

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

Transformations from the Parent Function

This page explores transformations of quadratic functions from the parent function y = x².

Transformations can include:

Vertical and horizontal shifts
Reflections
Vertical stretches or compressions

The page provides examples of graphing transformed quadratic functions and describing how they compare to the parent function.

Vocabulary: A transformation is a change to the size, shape, or position of a figure.

Example: The function y = $x + 2$ ² represents a shift of the parent function 2 units to the left.

Highlight: Understanding transformations is crucial for quickly sketching quadratic functions and predicting their behavior based on their equation.

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

Writing Equations and Putting It All Together

This final page combines all the concepts learned to write equations based on described transformations.

Key points about the vertex form y = a $x - h$ ² + k:

h represents the horizontal shift $positive h shifts left, negative h shifts right$
k represents the vertical shift $positive k shifts up, negative k shifts down$
If a is negative, the function is reflected over the x-axis
|a| > 1 represents a vertical stretch, while 0 < |a| < 1 represents a vertical compression

The page includes practice problems for writing equations based on described transformations from the parent function.

Example: A function translated 3 units left and 4 units down can be represented as y = $x + 3$ ² - 4.

Highlight: Being able to write equations based on described transformations demonstrates a deep understanding of how the coefficients and constants in a quadratic equation affect its graph.

Vocabulary: Vertical stretch occurs when |a| > 1, while vertical compression occurs when 0 < |a| < 1 in the vertex form of a quadratic equation.

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

Graphing Quadratic Equations

This page introduces the steps to graph a quadratic equation and provides examples for practice.

To graph a quadratic equation:

Find the axis of symmetry using the formula x = -b/ $2a$
Calculate the vertex
Create a table of values
Plot points and connect them into a smooth parabola

The page includes practice problems for graphing quadratic equations and identifying key features such as the axis of symmetry, vertex, domain, and range.

Example: For y = x² + 2x - 1, the axis of symmetry is x = -1, and the vertex is $-1, -2$ .

Vocabulary: Domain refers to all possible x-values, while range refers to all possible y-values of the function.

Highlight: Understanding how to graph quadratic equations is crucial for visualizing their behavior and identifying important characteristics.

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

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user