Quadratic Modeling

4.3 - Modeling With Quadratic Functions

Quadratic Model

• A quadratic function that represents a real data set

• Models are useful for making estimates

• Three noncollinear points define a quadratic function. Create a model using technology or by solving a system of three equations

Open Ended

Write a quadratic function that models the data:

(Hint: solve the system of three equations for the values of a, b, and c).

What if we used technology to check our answer?

Click the link to match the curve to the points: https://www.desmos.com/calculator/ubnj3ywu1m

Open Ended

Write the equation of the quadratic using the parameters from the Desmos graph:

As a note, Desmos can also generate an equation using a quadratic regression.

Poll

Which method was easier to use to write the quadratic?

• Writing and solving a system of three equations in three variables

• Using technology to match the curve

• Is this a trick question?

Open Ended

The prices for a one-topping pizza at the local pizza place are:

12 inch: $9.95

14 inch: $13.95

16 inch: $16.95

Use the Desmos graphing calculator to write a quadratic model for the price of different sizes of pizza. Use your model to estimate the cost of an 18 inch, one-topping pie.