3.2 Quadratic Functions--Connecting Intercepts and Linear Factors (Due 11/14/24)

Day 1 11/10/25

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

10

Guided Practice:
Connecting intercepts and factors

Graph the Function y=(x − 3)(x + 5)
Where does the parabola intercept (cross) the x-axis?
x=_______ and x=_______ 

Required

5

Connecting intercepts and factors

Graph the Function y=(x + 6)(x - 1)
Where does the parabola intercept (cross) the x-axis?
x=_______  and x=_______ 

Required

5

Connecting intercepts and factors

Graph the Function y=2(x - 8)(x - 8)

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

Required

10

Connecting intercepts and factors

Graph the Function y=-6(x + 3)(x)

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

Required

10

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


1) What are the x-intercepts? (Where the graph crosses the x-axis) 
x=_______  and  x=_______ 
2) What is the axis of symmetry? (The middle of the parabola, put your hands together)
x=_______ 

Required

10

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


1) What are the x-intercepts? (Where the graph crosses the x-axis) 
x=_______  and  x=_______ 
2) What is the axis of symmetry? (The middle of the parabola, put your hands together)
x=_______ 

Required

10

Graph the Function y=2(x + 7)(x - 3)


1) What are the x-intercepts? (Where the graph crosses the x-axis) 
x=_______  and  x=_______ 
2) What is the axis of symmetry? (The middle of the parabola, put your hands together)
x=_______ 

Required

10

Graph the function y=(x - 4)(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

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 (use coordinate form)
_______ 
Right x-intercept (use coordinate form)
_______ 
Axis of Symmetry (use x=___ form)
_______ 
Vertex (use coordinate form)
_______ 

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 (use coordinate form)
_______ 
Right x-intercept (use coordinate form)
_______ 
Axis of Symmetry (use x=___ form)
_______ 
Vertex (use coordinate form)
_______ 

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?_______ 

How high does the football get?_______ 

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._______ 

How many seconds does it take to reach its highest point?_______ 

Graph the function to answer the question.

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? (Round your answer to the nearest hundredth)

t=_______ 

Graph the quadratic equation to help you answer the question.

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 (use coordinate form)
_______ 
Right x-intercept (use coordinate form)
_______ 
Axis of Symmetry (use x=___ form)
_______ 
Vertex (use coordinate form)
_______ 

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 (use coordinate form)
_______ 
Right x-intercept (use coordinate form)
_______ 
Axis of Symmetry (use x=___ form)
_______ 
Vertex (use coordinate form)
_______ 

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 (use coordinate form)
_______ 
Right x-intercept (use coordinate form)
_______ 
Axis of Symmetry (use x=___ form)
_______ 
Vertex (use coordinate form)
_______ 

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 (use coordinate form)
_______ 
Right x-intercept (use coordinate form)
_______ 
Axis of Symmetry (use x=___ form)
_______ 
Vertex (use coordinate form)
_______ 

Day 2 11/12/25

 Solving Review

Required

10

Solve this linear equation.

Required

10

What does is it mean to solve an equation?

Solving Quadratic Equations by Graphing

Required

5

Click on the x-intercepts to this quadratic equation.

Required

10

Sometimes x-intercepts are called the "zeroes" of a equation. Based on the graph of quadratic equations why do you think that is?

Required

5

How many intercepts can a quadratic equation have?

Required

5

How many zeroes can a quadratic equation have?

Required

10

When the graph of an equation crosses the x-axis it is called an  __________

Another name for an x-intercept is a __________.

The reason it is called a zero is because the graph crosses the x-axis when the y-value of the equation is __________.

Another name for when y=0 is the __________ of the equation.

Required

5

Click on the solutions to this quadratic equation.

Required

20

Find the x-intercepts the following Quadratic function:
y=(x - 7)(x + 7)

x-intercepts
x=_______ 
x=_______ 

Solve the quadratic equation (x - 7)(x + 7)=0 ←(this is when y=0)

Left solution
_______ 
Right solution
_______ 

Required

10

What is the difference between the solutions to a quadratic equation and its x-intercepts?

Required

5

How many solutions can a quadratic equation have?

Required

10

What are the intercepts to this quadratic equation

Left Intercept:
_______ 
Right Intercept: 
_______ 

Required

10

What are the zeroes to this quadratic equation

Left Solution:
_______ 
Right Solution: 
_______ 

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

Draw an example of a quadratic equation with 0 solutions.

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

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=_______ 

3.2 Quadratic Functions--Connecting Intercepts and Linear Factors (Due 11/14/24)

Day 1 11/10/25

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.

x=_______ and x=_______

Graph the function y=(x - 4)(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.

Day 2 11/12/25

Solving Review

Solve this linear equation.

What does is it mean to solve an equation?

Solving Quadratic Equations by Graphing

Click on the x-intercepts to this quadratic equation.

Sometimes x-intercepts are called the "zeroes" of a equation. Based on the graph of quadratic equations why do you think that is?

How many intercepts can a quadratic equation have?

How many zeroes can a quadratic equation have?

Click on the solutions to this quadratic equation.

What is the difference between the solutions to a quadratic equation and its x-intercepts?

How many solutions can a quadratic equation have?

Draw an example of a quadratic equation with 0 solutions.

Day 1 11/10/25

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.

x=_______ and x=_______

Graph the function y=(x - 4)(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.

Day 2 11/12/25

Solving Review

Solve this linear equation.

What does is it mean to solve an equation?

Solving Quadratic Equations by Graphing

Click on the x-intercepts to this quadratic equation.

Sometimes x-intercepts are called the "zeroes" of a equation. Based on the graph of quadratic equations why do you think that is?

How many intercepts can a quadratic equation have?

How many zeroes can a quadratic equation have?

Click on the solutions to this quadratic equation.

What is the difference between the solutions to a quadratic equation and its x-intercepts?

How many solutions can a quadratic equation have?

Draw an example of a quadratic equation with 0 solutions.

x=_ and x=_

Guided Practice
Graph the function using its intercepts.

x=_ and x=_

Guided Practice
Graph the function using its intercepts.