1. Quadratic Regression

2. The human cannonball!

3. Lots of real word phenomena can be modeled with a quadratic function
Lots of real word phenomena can be modeled with a quadratic function. You’ve seen this with the path of a football. What are some more real life examples of parabolas?

4. Quadratic Regression
We can use our calculators to find a quadratic equation that models real-life data. This equation is called a quadratic regression.

5. Quadratic Regression Steps
STAT → Edit… Enter the data in L1 and L2.
STAT → CALC → QuadReg (Don’t hit Enter)
VARS → Function → Y-Vars → Y1
Enter
You now have a quadratic regression! If you look in Y1, your calculator has entered the equation for you!

6. Example 1
The table shows the monthly sales (thousands) for a new hair salon since its grand opening in March. 1) Find the best fitting quadratic model. 2) What will the total sales be 7 months after opening?
Month, t 1 2 3 4 5
Sales. S
5.6
5.8
6.2
6.9
7.9
9.0

7. Example 2
The table shows the height of a model rocket after it is fired upwards from the ground. 1) Find the best fitting quadratic model. 2) When does the rocket hit the ground?
Time (seconds)
Height (feet)
0.5
20.5 1
31.36
1.5
36.25 2
30.41
2.5
28.23

8. Example 3
The table shows the rate of oxygen consumed by an athlete running at a speed of 16 km/h using various stride lengths. 1) Find the best fitting quadratic model. 2) What is the vertex of the model? What does it mean to the runner?
Stride Length (cm)
Oxygen Consumption (L/min)
135
4.03
149
3.87
169
4.52
175
4.92