Subjects

Algebra 1

Quadratics

Vertex Form

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

Name: Knowunity
Brand: Knowunity

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

Olivia ingalls

@oliviaingalls_okwr

0 Follower

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 these concepts.

Key points:

Converting standard form (ax² + bx + c) to vertex form (a(x-h)² + k)
Graphing quadratic equations using tables and identifying key features
Understanding transformations of quadratic functions from the parent function
Writing equations based on described transformations

4/18/2023

439

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

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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 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.

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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.

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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.

View

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.

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.

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

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Students use Knowunity

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Subjects

Algebra 1

Quadratics

Vertex Form

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

Olivia ingalls

@oliviaingalls_okwr

0 Follower

Key points:

Converting standard form (ax² + bx + c) to vertex form (a(x-h)² + k)
Graphing quadratic equations using tables and identifying key features
Understanding transformations of quadratic functions from the parent function
Writing equations based on described transformations

4/18/2023

439

Algebra 1

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.

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.

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