8.12.2 Finding the Curve of Best Fit

Examine the data set and graph given in the Desmos graphing tool below.

Examine the data. Do they appear to you to form a line or a curve?

We will use graphing technology to find a curve of best fit. Click the pointer below the table into entry box #2 to enter a new function. The cursor should start blinking. Enter the equation:

$y_1~a{x}_1^2+b{x}_1+c$

• Notice that when you type the 1 after $y$ or $x$, Desmos automatically places it as subscript.

• Also notice that we are not using an equal sign. The symbol ~ means approximately and tells Desmos to approximate a line or curve of best fit. It should be in the top-left corner of your keyboard, and you might press it using the Shift button. If you are using the Desmos on-screen keyboard, it will be on the ABC keyboard.

• After pressing the subscript 1 after the $y$ and the first $x$, use the ^ symbol to tell Desmos you would like to enter an exponent.

1. Once you have entered the curve of best fit, you can press Enter. The curve of best fit will appear. Your screen will look like this:

Look in the lower-left corner of the screen. We will use the $a$, $b$, and $c$ values to construct the equation for our curve of best fit.

Write an equation in the form $y=a{x}^2+bx+c$ for the curve of best fit using the values you found.