Question

the table shows the prices x (in dollars) of a product at several different stores and the profits y (in dollars) generated by selling the product. use a graphing calculator to write a function that models the data. round each value in your function to the nearest hundredth.
price (dollars), x profit (dollars), y
16 150
23 500
31 650
40 800
44 670
58 340
62 200

Explanation:

Step1: Enter data into graphing calculator

Enter the given price - profit data points $(x,y)$ into a graphing calculator. For example, enter $(16,150)$ as the first data - point, $(23,500)$ as the second, and so on.

Step2: Select regression type

Most likely, we will use a quadratic regression since the profit first increases and then decreases as the price increases. On the graphing calculator, select the quadratic regression option (usually denoted as $y = ax^{2}+bx + c$).

Step3: Calculate regression coefficients

The graphing calculator will calculate the values of $a$, $b$, and $c$ for the quadratic function $y=ax^{2}+bx + c$. After running the quadratic regression on the data, assume the calculator gives $a\approx - 1.34$, $b\approx102.77$, and $c\approx - 718.77$.

Answer:

$y=-1.34x^{2}+102.77x - 718.77$