3.2 Quadratic Functions--Connecting Intercepts and Linear Factors (Due 12/5/23)

Monday 11/14/23

Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?

Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.

Show your work for credit.

Required

5

Guided Practice:
Connecting intercepts and factors

Graph the Function y=(x − 3)(x + 5)

Where does the parabola intercept (cross) the x-axis?

Required

10

What is the connection between the x-intercepts of the function y = (x − 3)(x + 5) and the factors: (x − 3) and (x + 5)

Required

10

Graph the Function y=(x + 6)(x + 2)


1) What are the x-intercepts? (Where the graph crosses the x-axis)_______ 
2) What is the axis of symmetry? (The middle of the parabola)_______ 

Required

10

Graph the function y=(x + 6)(x + 2). What is the relationship between the axis of symmetry and its intercepts?

Required

20

Guided Practice
Graph the function using its intercepts.

Required

10

Graph the function using its intercepts.

Required

10

Graph the function using its intercepts.

Required

10

Graph the function using its intercepts.

Required

20

Guided Practice: Find the x-intercepts of this quadratic function without graphing it:

Required

10

Find the x-intercepts of this quadratic function without graphing it:

Required

15

Guided Practice: Graphing and Interpreting Quadratic Functions

The height of a football after it has been kicked from the top of a hill can be modeled by the equation:

Where h is the height of the football in feet and t is the time in seconds. How long is the football in the air?

Graph the function to answer the question.

Required

15

Graphing and Interpreting Quadratic Functions:
The height of a flare fired from the deck of a ship can be modeled by h = (−4t + 24)(4t + 4) where h is the height of the flare above water in feet and t is the time in seconds. Find the number of seconds it takes the flare to hit the water.
Graph the function to answer the question.

Day 2 11/15/23

Review

Required

10

Solve this linear equation.

Required

10

Solve this linear equation.

Solving Quadratic Equations by Graphing

Required

10

Solve this quadratic equation graphing

x=_______ 
x=_______ 

Required

10

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

10

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

10

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

10

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

10

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

10

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

10

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

20

A bird is in a tree 30 feet off the ground and drops a twig that lands on a
rosebush 25 feet below. The function h (t) = -16t²+ 30, where t represents the time
in seconds, gives the height h, in feet, of the twig above the ground as it falls. When
will the twig land on the bush?


Solve this quadratic equation graphing.

t=_______ 

Required

20

A trampolinist steps off from 15 feet above ground to a trampoline 13 feet
below. The function h (t) = -16 t²+ 15, where t represents the time in seconds, gives
the height h, in feet, of the trampolinist above the ground as he falls. When will the
trampolinist land on the trampoline?


Solve this quadratic equation graphing.

t=_______ 

Monday 11/27/23

Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?

Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.

Show your work for credit.

Required

20

Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

 Left x-intercept
_______ 
Right x-intercept
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 

Required

20

Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

 Left x-intercept
_______ 
Right x-intercept
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 

Required

20

Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

 Left x-intercept
_______ 
Right x-intercept
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 

Required

20

Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

 Left x-intercept
_______ 
Right x-intercept
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 

Required

20

Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

 Left x-intercept
_______ 
Right x-intercept
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 

Required

20

Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

 Left x-intercept
_______ 
Right x-intercept
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 

Day 2 11/29/23

Spiral Review

Required

10

Mutlitply the binomials:

Required

10

Mutlitply the binomials:

Required

10

Factor each expression. Be sure to check for a GCF first.

Required

10

Factor each expression. Be sure to check for a GCF first.

Required

10

Factor each expression. Be sure to check for a GCF first.

Required

10

Factor each expression. Be sure to check for a GCF first.

Day 3 11/30/23

Spiral Review

Required

10

Solve this equation:

6x-9=45

Required

10

What does is it mean to solve an equation?

Solving Quadratics

Required

10

Solve the following Quadratic function:
(2x + 3)(x + 1) = 0

x=_______ 

x=_______ 

Required

10

Solve the following Quadratic function:
x(8x + 3) = 0

x=_______ 
x=_______ 

Required

10

Solve the following Quadratic function:
(x - 7)(x + 7) = 0

x=_______ 
x=_______ 

Required

10

Solve the following Quadratic function:
2x2 + 5x + 2 = 0

x=_______ 
x=_______ 

Required

10

Solve the following Quadratic function:
3x2 + 22x + 35 = 0

x=_______ 
x=_______ 

Required

10

Solve the following Quadratic function:
7x2 - 60x + 32 = 0
x=_______ 
x=_______ 

Required

10

Factor and solve:
3x2 - x - 14 = 0
x=_______ 
x=_______ 

Required

10

Factor and solve:
3x2 + 17x - 28 = 0

x=_______ 
x=_______ 

Day 4 12/4/23

Solving Quadratic Word Problem

Calculating Room Areas
People frequently need to calculate the area of rooms, boxes or plots of land. An example might involve building a rectangular box where one side must be twice the length of the other side.

For example, if you have only 4 square feet of wood to use for the bottom of the box, with this information, you can create an equation for the area of the box using the ratio of the two sides. This means the area -- the length times the width -- in terms of x would equal x times 2x, or 2x2. This equation must be less than or equal to four to successfully make a box using these constraints.

Required

10

Required

10

Required

10

Required

10

Required

10

Objects Affected by Gravity

Required

30

Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t²+ 16t + 480 , where t is the time in seconds and h is the height in feet.

How long did it take for Jason to reach his maximum height?_______ 

What was the highest point that Jason reached?_______ 

Jason hit the water after how many seconds?_______

Required

40

3.2 Quadratic Functions--Connecting Intercepts and Linear Factors (Due 12/5/23)

Monday 11/14/23

Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?

Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.

Show your work for credit.

Guided Practice:Connecting intercepts and factorsGraph the Function y=(x − 3)(x + 5)Where does the parabola intercept (cross) the x-axis?

What is the connection between the x-intercepts of the function y = (x − 3)(x + 5) and the factors: (x − 3) and (x + 5)

Graph the function y=(x + 6)(x + 2). What is the relationship between the axis of symmetry and its intercepts?

Guided PracticeGraph the function using its intercepts.

Graph the function using its intercepts.

Graph the function using its intercepts.

Graph the function using its intercepts.

Guided Practice: Find the x-intercepts of this quadratic function without graphing it:

Find the x-intercepts of this quadratic function without graphing it:

Guided Practice: Graphing and Interpreting Quadratic Functions

Day 2 11/15/23

Review

Solve this linear equation.

Solve this linear equation.

Solving Quadratic Equations by Graphing

Monday 11/27/23

Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?

Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.

Show your work for credit.

Day 2 11/29/23

Spiral Review

Mutlitply the binomials:

Mutlitply the binomials:

Factor each expression. Be sure to check for a GCF first.

Factor each expression. Be sure to check for a GCF first.

Factor each expression. Be sure to check for a GCF first.

Factor each expression. Be sure to check for a GCF first.

Day 3 11/30/23

Spiral Review

Solve this equation:6x-9=45

What does is it mean to solve an equation?

Solving Quadratics

Day 4 12/4/23

Solving Quadratic Word Problem

Calculating Room Areas

Objects Affected by Gravity

Monday 11/14/23

Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?

Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.

Show your work for credit.

Guided Practice:Connecting intercepts and factorsGraph the Function y=(x − 3)(x + 5)Where does the parabola intercept (cross) the x-axis?

What is the connection between the x-intercepts of the function y = (x − 3)(x + 5) and the factors: (x − 3) and (x + 5)

Graph the function y=(x + 6)(x + 2). What is the relationship between the axis of symmetry and its intercepts?

Guided PracticeGraph the function using its intercepts.

Graph the function using its intercepts.

Graph the function using its intercepts.

Graph the function using its intercepts.

Guided Practice: Find the x-intercepts of this quadratic function without graphing it:

Find the x-intercepts of this quadratic function without graphing it:

Guided Practice: Graphing and Interpreting Quadratic Functions

Day 2 11/15/23

Review

Solve this linear equation.

Solve this linear equation.

Solving Quadratic Equations by Graphing

Monday 11/27/23

Essential Question: How are the x-intercepts of a quadratic function and its linear factors related?

Learning Target: Students will be able to identify the x-intercepts of quadratic equations and use them to create graphical representations of those functions.

Show your work for credit.

Day 2 11/29/23

Spiral Review

Mutlitply the binomials:

Mutlitply the binomials:

Factor each expression. Be sure to check for a GCF first.

Factor each expression. Be sure to check for a GCF first.

Factor each expression. Be sure to check for a GCF first.

Factor each expression. Be sure to check for a GCF first.

Day 3 11/30/23

Spiral Review

Solve this equation:6x-9=45

What does is it mean to solve an equation?

Solving Quadratics

Day 4 12/4/23

Solving Quadratic Word Problem

Guided Practice:
Connecting intercepts and factors

Graph the Function y=(x − 3)(x + 5)

Where does the parabola intercept (cross) the x-axis?

Guided Practice
Graph the function using its intercepts.

Solve this equation:

6x-9=45

Guided Practice:
Connecting intercepts and factors

Graph the Function y=(x − 3)(x + 5)

Where does the parabola intercept (cross) the x-axis?

Guided Practice
Graph the function using its intercepts.

Solve this equation:

6x-9=45