Topic: Graphing Quadratic Functions
Grade: 9th
Section: 10-1

Materials: calculators, worksheets, chalkboard/whiteboard, chalk/markers
**ALL WORKSHEETS WILL BE PROVIDED

Lesson Overview: Students will learn how to graph quadratic functions, both by hand and by using the calculator.  They will also find the equation of the axis of symmetry and the coordinates of the vertex of a parabola.  Students will work through a series of questions first as a class and then independently.

Lesson Objectives:
•	Students will be able to identify the equation of a parabola, and then create graphs of parabolas by plotting ordered pairs. [Application]
•	Students will analyze the graphs of parabolas in order to find the maximum/minimum point (vertex), as well as the axis of symmetry. [Analysis]
•	Given an equation for a parabola the students will be able to write the equation of the axis of symmetry, find the coordinates of the vertex, identify whether it is a maximum or minimum, and then graph the function. [Evaluation]

NYS Standards:
•	Key Idea 7: Patterns/Functions- Students apply linear, and quadratic functions in the solution of problems.
•	Key Idea 7: Patterns/Functions-Students represent and analyze functions using verbal descriptions, tables, equations and graphic forms of functions.

Anticipatory Set: (3 mins)
Ask the students what it looks like when you bounce a ball to another person.  Draw on the board a ball bouncing (this should look like a parabola).  Then ask the students what it looks like when someone dives into a pool, touches the bottom and then swims back up to the top.  Draw this on the board (again this should look like a parabola).

Developmental Activity: (27 mins)
1.)	Tell the students that the function describing the ball bouncing or diving in the pool is an example of a quadratic function.
2.)	Pass out “Graphing Quadratic Functions”.  
3.)	After introducing the standard form of a quadratic function- point out to the students that this polynomial is of degree 2 and the exponents are positive.
4.)	For example 1- Ask the students what they notice about the y-values. (they should notice the pattern in which they repeat)
5.)	For example 2- Ask the students why the graph opens downward.
6.)	Ask the students what it means for something to be symmetrical. (a figure can be folded in half so that each half matches the other exactly)
7.)	Show the students how to graph both examples on the calculator.  
8.)	Point out how to find the vertex on the calculator.

Closure: (5 mins)
Discuss what they learned about what the axis of symmetry is.  When does a parabola have a maximum? A minimum?  What is a vertex?  These are just a few suggestions.

Assessment: (5 mins)
Have the students complete the Exit Ticket and hand it in before they leave. This will be graded.

Name:	Answer Key								Date:

“Graphing Quadratic Functions”

A QUADRATIC FUNCTION can be written in the form , where .
This form of the quadratic function is called STANDARD FORM.  The graph of a quadratic function is called a PARABOLA.

A parabola can either open UPWARD or DOWNWARD.

1.) Graph Opens Upward
Use a table of values to graph .
x	y	
 -2	11	
-1	1	
0	-5	
1	-7	
2	-5	
3	1	
4	11	

Consider the standard form of a quadratic equation for this example.  The value of  “a” is POSITIVE and the curve opens UPWARD.

The lowest point on the graph is called the MINIMUM.

What is the minimum of this graph?  (1, -7)

2.) Graph Opens Downward
Use the table of values to graph .
x	y	
-1	-6	
0	-1	
1	2	
2	3	
3	2	
4	-1	
5	-6	

The value of  “a” is NEGATIVE, and the curve opens DOWNWARD.
Therefore the graph has a highest point, called the MAXIMUM.
What is the maximum for this graph? (2,3)
**The maximum and minimum point of a parabola is called the VERTEX.

Parabolas are symmetrical figures.  They have an axis of symmetry.  The VERTEX is the only point on the parabola that is on the axis of symmetry.  The axis of symmetry is written as x = the x-value of the vertex.

What is the axis of symmetry for the parabola in example 1? X =1
What is the axis of symmetry for the parabola in example 2? X =2

Name:											Date:

“Graphing Quadratic Functions”

A _______________________ can be written in the form , where .
This form of the quadratic function is called ________________________.  The graph of a quadratic function is called a _________________.

A parabola can either open ________________or _________________.

1.) Graph Opens Upward
Use a table of values to graph .
x	y	
 -2	11	
-1	1	
0	-5	
1	-7	
2	-5	
3	1	
4	11	

Consider the standard form of a quadratic equation for this example.  The value of  “a” is ________________ and the curve opens ______________.

The lowest point on the graph is called the _________________.

What is the minimum of this graph?  

2.) Graph Opens Downward
Use the table of values to graph .
x	y	
-1	-6	
0	-1	
1	2	
2	3	
3	2	
4	-1	
5	-6	

The value of  “a” is _________________, and the curve opens ___________________.
Therefore the graph has a highest point, called the ___________________.
What is the maximum for this graph? 
**The maximum and minimum point of a parabola is called the ____________.

Parabolas are symmetrical figures.  They have an axis of symmetry.  The ____________ is the only point on the parabola that is on the axis of symmetry.  The axis of symmetry is written as x = the x-value of the vertex.

What is the axis of symmetry for the parabola in example 1? 
What is the axis of symmetry for the parabola in example 2? 

Name:	Answer Key							Date:

Exit Ticket

Graph the equation , using the table.
X	Y	
-2	-5	
-1	0	
0	3	
1	4	
2	3	
3	0	
4	-5	

What are the coordinates of the vertex? (1,4)

Write the equation of the axis of symmetry?  X=1

Is the vertex a maximum or minimum?  Maximum

Name:										Date:

Exit Ticket

Graph the equation , using the table.
X	Y	
-2	-5	
-1	0	
0	3	
1	4	
2	3	
3	0	
4	-5	

What are the coordinates of the vertex? 

Write the equation of the axis of symmetry?

Is the vertex a maximum or minimum?