3.1 Exploring Quadratic Functions (Due 11/4/24)

Last updated 15 days ago

34 questions

Required

3.1 Exploring Quadratic Functions (Due 11/4/24)

Last updated 15 days ago

34 questions

Essential Question:  What are quadratic functions and how can I graph them?

Learning Target:  Students will be able to recognize the critical characteristics of the graph of quadratic functions and create the graph representing quadratic functions.

Show your work for full credit. 

Remember to use complete sentences when answering written answers.

Day 1 11/4/25

Exploring Graphing Quadratic Functions

Warm-Up
What are the critical values of this absolute value function:

y=2|x+2|+2 

2) Use the critical values of this equation to graph it.

Opens (upward or downward)
 _______ 
Vertex (h,k)
_______ 
Axis of Symmetry ( x=__ )
_______ 

Required

Warm-Up
Fill out the table and use the graph on the left to create a parabola from the quadratic function:

Required

List one way that the graph of the absolute function is the same as the quadratic function?_______

 What is one way that the graph of the absolute function is different from the quadratic function?_______

Required

Exploration

How does the a affect the function 

compared to the original function

What happens to the function when a>1
_______ 

What happens to the function when a<0 (negative)
_______ 

Required

Exploration
How does the h affect the function 
compared to the original function

What happens to the function when h is positive?
_______ 
What happens to the function when h is negative?
_______ 

Required

Exploration
How does the k affect the function 
compared to the original function

What happens to the function when k is positive?
_______ 
What happens to the function when k is negative?
_______ 

Required

Based on your explorations, the quadratic equation:

has a horizontal shift __________ of __________ spaces and a vertical shift__________ of __________ spaces and is pointed __________

Features of Quadratic Functions

Required

Use the internet to answer these questions:

All quadratic functions are "U" shaped. What is another term that describes the shape of a quadratic function?

Required

Use the internet to answer these questions:

What is the name of the middle point of a quadratic function?

Required

Use the internet to answer these questions:

The lowest point of a parabola it is called the __________?

Required

Use the internet to answer these questions:

The line that runs through the middle of the parabola is called the ____ _ _______?

Required

The axis of symmetry of a quadratic function sometimes does not pass through the vertex?

Required

What is the vertex of this parabola? Name the coordinate.
_______ 

Required

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

Required

What is the vertex of this parabola? Name the coordinate.

Required

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

Required

What is the vertex of this parabola? Name the coordinate.

Required

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

Required

What does the vertex of this quadratic function represent?

Day 2 11/5/25

Essential Question: How do transformations effect the parent function:

Learning target: Students will use the vertex formula:

to make transformations to the parent function:

Show work for credit

More Features of Quadratic Functions

Required

Fill out the table and use the graph on the left to create a parabola from the quadratic function:

Required

How do negative values for a affect the function
compared to the original function

Required

Guided Practice: Stretching Quadratic Functions

Fill out the table and use the graph on the left to create a parabola from the quadratic function:

Required

How do inputting numbers between 0 and 1 for a affect the function
compared to the original function

Required

Describe the transformation of:
Stretch or Compression?(If a=1 or a=-1, then write none)_______ 
Opens upward or downward?_______ 
Horizontal shift? (If there is no shift write none)_______ 
Vertical shift? (If there is no shift write none)_______ 
Axis of Symmetry? (x=h)_______ 
Vertex (h,k)_______ 

Required

Describe the transformation of:

Stretch or Compression?(If a=1 or a=-1, then write none)_______ 
Opens upward or downward?_______ 
Horizontal shift? (If there is no shift write none)_______ 
Vertical shift? (If there is no shift write none)_______ 
Axis of Symmetry? (x=h)_______ 
Vertex (h,k)_______ 

Required

Describe the transformation of:




Stretch or Compression?(If a=1 or a=-1, then write none)_______ 
Opens upward or downward?_______ 
Horizontal shift? (If there is no shift write none)_______ 
Vertical shift? (If there is no shift write none)_______ 
Axis of Symmetry? (x=h)_______ 
Vertex (h,k)_______ 

Required

Describe the transformation of:

Stretch or Compression?(If a=1 or a=-1, then write none)_______ 
Opens upward or downward?_______ 
Horizontal shift? (If there is no shift write none)_______ 
Vertical shift? (If there is no shift write none)_______ 
Axis of Symmetry? (x=h)_______ 
Vertex (h,k)_______ 

Required

Describe the transformation of:
Stretch or Compression?(If a=1 or a=-1, then write none)_______ 
Opens upward or downward?_______ 
Horizontal shift? (If there is no shift write none)_______ 
Vertical shift? (If there is no shift write none)_______ 
Axis of Symmetry? (x=h)_______ 
Vertex (h,k)_______ 

Graphing Quadratic Equations

Required

Guided Practice: Graph the function and state the vertex.

Required

Graph this function:

Required

Graph this function:

Required

Graph the function and state the vertex.

Required

3.1 Exploring Quadratic Functions (Due 11/4/24)

3.1 Exploring Quadratic Functions (Due 11/4/24)

Essential Question: What are quadratic functions and how can I graph them?

Learning Target: Students will be able to recognize the critical characteristics of the graph of quadratic functions and create the graph representing quadratic functions.

Show your work for full credit.

Remember to use complete sentences when answering written answers.

Day 1 11/4/25

Exploring Graphing Quadratic Functions

Warm-Up

Warm-UpFill out the table and use the graph on the left to create a parabola from the quadratic function:

Warm-Up

Exploration

Exploration

Exploration

Features of Quadratic Functions

Use the internet to answer these questions:All quadratic functions are "U" shaped. What is another term that describes the shape of a quadratic function?

Use the internet to answer these questions:What is the name of the middle point of a quadratic function?

Use the internet to answer these questions:The lowest point of a parabola it is called the __________?

Use the internet to answer these questions:The line that runs through the middle of the parabola is called the ______ ___ _______?

The axis of symmetry of a quadratic function sometimes does not pass through the vertex?

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

What is the vertex of this parabola? Name the coordinate.

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

What is the vertex of this parabola? Name the coordinate.

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

What does the vertex of this quadratic function represent?

Day 2 11/5/25

Essential Question: How do transformations effect the parent function:

Learning target: Students will use the vertex formula:

to make transformations to the parent function:

Show work for credit

More Features of Quadratic Functions

Fill out the table and use the graph on the left to create a parabola from the quadratic function:

How do negative values for a affect the function compared to the original function

Guided Practice: Stretching Quadratic FunctionsFill out the table and use the graph on the left to create a parabola from the quadratic function:

Guided Practice: Stretching Quadratic Functions

How do inputting numbers between 0 and 1 for a affect the function compared to the original function

Graphing Quadratic Equations

Guided Practice: Graph the function and state the vertex.

Guided Practice: Graph the function and state the vertex.

Graph this function:

Graph this function:

Graph this function:

Graph this function:

Graph the function and state the vertex.

Graph the function and state the vertex.

Graph the function and state the vertex.

Graph the function and state the vertex.

Essential Question: What are quadratic functions and how can I graph them?

Learning Target: Students will be able to recognize the critical characteristics of the graph of quadratic functions and create the graph representing quadratic functions.

Show your work for full credit.

Remember to use complete sentences when answering written answers.

Day 1 11/4/25

Exploring Graphing Quadratic Functions

Warm-Up

Warm-UpFill out the table and use the graph on the left to create a parabola from the quadratic function:

Warm-Up

Exploration

Exploration

Exploration

Features of Quadratic Functions

Use the internet to answer these questions:All quadratic functions are "U" shaped. What is another term that describes the shape of a quadratic function?

Use the internet to answer these questions:What is the name of the middle point of a quadratic function?

Use the internet to answer these questions:The lowest point of a parabola it is called the __________?

Use the internet to answer these questions:The line that runs through the middle of the parabola is called the ______ ___ _______?

The axis of symmetry of a quadratic function sometimes does not pass through the vertex?

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

What is the vertex of this parabola? Name the coordinate.

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

What is the vertex of this parabola? Name the coordinate.

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

What does the vertex of this quadratic function represent?

Day 2 11/5/25

Essential Question: How do transformations effect the parent function:

Learning target: Students will use the vertex formula:

to make transformations to the parent function:

Show work for credit

More Features of Quadratic Functions

Fill out the table and use the graph on the left to create a parabola from the quadratic function:

How do negative values for a affect the function compared to the original function

Warm-Up
Fill out the table and use the graph on the left to create a parabola from the quadratic function:

Use the internet to answer these questions:

All quadratic functions are "U" shaped. What is another term that describes the shape of a quadratic function?

Use the internet to answer these questions:

What is the name of the middle point of a quadratic function?

Use the internet to answer these questions:

The lowest point of a parabola it is called the __________?

Use the internet to answer these questions:

The line that runs through the middle of the parabola is called the ____ _ _______?

How do negative values for a affect the function
compared to the original function

Guided Practice: Stretching Quadratic Functions

Fill out the table and use the graph on the left to create a parabola from the quadratic function:

How do inputting numbers between 0 and 1 for a affect the function
compared to the original function

Warm-Up
Fill out the table and use the graph on the left to create a parabola from the quadratic function:

Use the internet to answer these questions:

All quadratic functions are "U" shaped. What is another term that describes the shape of a quadratic function?

Use the internet to answer these questions:

What is the name of the middle point of a quadratic function?

Use the internet to answer these questions:

The lowest point of a parabola it is called the __________?

Use the internet to answer these questions:

The line that runs through the middle of the parabola is called the ____ _ _______?

How do negative values for a affect the function
compared to the original function

Guided Practice: Stretching Quadratic Functions

Fill out the table and use the graph on the left to create a parabola from the quadratic function:

How do inputting numbers between 0 and 1 for a affect the function
compared to the original function