Lesson 1 – Quadratics Data and Graphs
Objectives:



To understand the difference between linear, exponential and quadratic data.
To understand what quadratic looks like in graphical form
To understand what quadratic looks like in algebraic form
Warm up and Review – Which of these functions are linear, exponential or neither? Show how you can tell.
Data
How can I tell?
Function ____________________________
Equation ______________________
Function ____________________
Equation ______________________
Function ____________________________
Equation ______________________
Function ____________________________
Equation ______________________
Function ____________________________
Equation ______________________
Lesson 1 – Quadratics Data and Graphs
Explore the two data sets that are neither. What connections do you see between the data? Explain.
Write a 3rd data set that has the same type of relationship as the other two.
x
y
Set up suitable axes and plot your data set on the grid below. Explain what it looks like.
This Data represents a Quadratic Model. What do I know about Quadratic data?
Technology – Let’s look at the other two data sets on our GDC.
Go to STAT – EDIT to enter the data
Enter the x/y data in L1 and L2
Write the equation of the two data sets in the table above.
STAT - CALC – 5 (QUADREG)
Lesson 1 – Quadratics Data and Graphs
Exploration 1
Mr. Brown enjoys vegetable gardening and is digging a garden this weekend. He plans to dig his garden this
weekend. He has a total of 12 m of fencing to enclose the rectangular garden to keep his dog from eating the
vegetables. He is able to use the wall of the
garage for one side of the garden.
Data
Graph
Explore the different lengths, widths and areas he could
have for his garden.
y
Area
15
10
5
length x
1
Problem: If Mr. Brown wanted to maximize the area of his
garden, what would he choose for the dimensions of his garden?
Explain your choice.
What does the solution look like on your graph?
2
3
4
5
6
7
Algebra - Could we write an equation for the area
A in terms of the length L?
Lesson 1 – Quadratics Data and Graphs
Exploration 2
Mr. Brown decides that he would rather have someone come in and dig the garden for him. When he looks at
where the garden is to be, the pool is in the way, and the width of the garden will need to be 1m shorter than
the length. He hires a gardener that charges $8 / square meter to dig the garden. Mr. Brown is worried, and
wants to minimize his costs.
Data
Graph
Explore the different lengths, widths and areas he could have
for his garden.
y
Area
15
10
5
Explore the different costs for the garden
length x
1
2
3
4
5
6
7
y
Cost
180
160
140
120
100
80
60
40
20
Lengthx
5
Problem: If Mr. Brown wanted to minimize the cost of his garden,
what would he choose for the dimensions of his garden? Explain
how you made your choice.
What does the solution look like on your graph(s)?
10
15
20
Algebra - Could we write an equation for the
Cost C in terms of the length L?
Lesson 1 – Quadratics Data and Graphs
Lesson 1 – Quadratics Data and Graphs