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

Last updated 12 months ago
50 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 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

Review Finding the Square of a Binomial

Required
20

Guided Practice:

Find the square of this binomial:

Required
20

Guided Practice:

Find the square of this binomial:

Converting Quadratic Equations from Vertex Form into Standard Form



Required
10

How do you convert Vertex Form into Standard Form?

Video Tutorial: Hot to convert Vertex Form into Standard Form

Required
20

Change the vertex form to standard quadratic form:

Required
20

Change the vertex form to standard quadratic form.

Required
10

Change the vertex form to standard quadratic form.

10

Change the vertex form to standard quadratic form.

10

Change the vertex form to standard quadratic form.

10

Change the vertex form to standard quadratic form.

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

Find the difference between these polynomials. (subtract them)