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 10/29/24

Exploring Graphing Quadratic Functions

10

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.

Required

20

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

Required

20

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

5

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

5

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?
_______ 

5

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

10

 Exit Ticket

The quadratic function 

has a horizontal shift of ____________________ and a vertical shift of____________________ and is pointed __________

Features of Quadratic Functions

Watch this video covering the basics about quadratic functions

Required

2

According to the video, all quadratic functions are "U" shaped. What is another term that describes the shape of a quadratic function?

Required

2

According to the video, what is the name of the middle point of a quadratic function? This point lies on the axis-of symmetry.

Required

2

According to the video, if the vertex is lowest point of a parabola it is called the __________?

Required

2

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

Required

5

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

Required

5

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

Required

5

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

Required

5

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

Required

5

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

Required

5

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

Required

10

What does the vertex of this quadratic function represent?

Day 2 10/30/24

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

30

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

Required

5

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

Required

20

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

5

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

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

Required

10

Required

12

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

12

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

12

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

12

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

12

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

10

Graph this function:

Required

10

Graph this function:

Required

30

Guided Practice: Graph the function and state the vertex.

Required

15

Graph the function and state the vertex.

Required

15

Graph the function and state the vertex.

Day 3 10/31/24

Essential Question: How can you change the vertex form of a quadratic function to standard form?

Learning Target: Students will be able to convert vertex form of a quadratic function into standard form of a quadratic function.

Exploring Standard Form of a Quadratic Equation:
How to find the Vertex in Standard Form

Essential Question: How can you change the vertex form of a quadratic function to standard form?

Learning Target: Students will be able to convert vertex form of a quadratic function into standard form of a quadratic function.

Required

20

Guided Practice: Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Required

20

Guided Practice: Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Required

20

Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Required

20

Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Day 4 11/1/24

Interpreting Vertex Form and Standard Form

Required

20

Required

20

Required

10

Required

20

Required

20

Required

10

Review

Required

10

Simplify this expression:

Required

2

Classify the polynomial below based on the number of terms.

Required

2

Classify the polynomial below based on its degree.

Required

10

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 10/29/24

Exploring Graphing Quadratic Functions

Warm-UpWhat 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.

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

Exit Ticket

Features of Quadratic Functions

According to the video, all quadratic functions are "U" shaped. What is another term that describes the shape of a quadratic function?

According to the video, what is the name of the middle point of a quadratic function? This point lies on the axis-of symmetry.

According to the video, if the vertex is lowest point of a parabola it 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 10/30/24

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

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

Graph this function:

Graph this function:

Graph this function:

Graph this function:

Guided Practice: Graph the function and state the vertex.

Guided Practice: 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.

Graph the function and state the vertex.

Day 3 10/31/24

Essential Question: How can you change the vertex form of a quadratic function to standard form?

Learning Target: Students will be able to convert vertex form of a quadratic function into standard form of a quadratic function.

Exploring Standard Form of a Quadratic Equation:

How to find the Vertex in Standard Form

Essential Question: How can you change the vertex form of a quadratic function to standard form?

Learning Target: Students will be able to convert vertex form of a quadratic function into standard form of a quadratic function.

Guided Practice: Graphing Standard FormWhat is the graph of the function? Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Guided Practice: Graphing Standard Form

Guided Practice: Graphing Standard FormWhat is the graph of the function? Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Guided Practice: Graphing Standard Form

Graphing Standard FormWhat is the graph of the function? Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Graphing Standard Form

Graphing Standard FormWhat is the graph of the function? Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Graphing Standard Form

Day 4 11/1/24

Interpreting Vertex Form and Standard Form

Review

Simplify this expression:

Classify the polynomial below based on the number of terms.

Classify the polynomial below based on its degree.

Find the difference between these polynomials. (subtract them)

Find the difference between these polynomials. (subtract them)

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 10/29/24

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.

Warm-Up
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 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

Guided Practice: Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Guided Practice: Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

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.

Warm-Up
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 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

Guided Practice: Graphing Standard Form

What is the graph of the function?

Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.