Question

3
select the correct answer from each drop - down menu
the annual enrollment of a university for the last nine years is recorded in the table
year 1 2 3 4 5 6 7 8 9
students (thousands) 9.5 8 8.5 7.5 6.5 6.5 8.5 9.5 9
what quadratic function best models this set of data?
y = (box) (x^{2}+box) (x+box)

Explanation:

Step1: Recall quadratic regression formula

The general form of a quadratic function is $y = ax^{2}+bx + c$. We can use a statistical software or a calculator with regression capabilities (like a TI - 84 Plus) to find the values of $a$, $b$, and $c$ for the given data points $(x_i,y_i)$ where $x_i$ represents the year ($i = 1,2,\cdots,9$) and $y_i$ represents the number of students in thousands.

Step2: Input data into calculator/software

Input the years as the $x$ - values (1, 2, 3, 4, 5, 6, 7, 8, 9) and the number of students (9.5, 8, 8.5, 7.5, 6.5, 6.5, 8.5, 9.5, 9) as the $y$ - values into the regression feature of the calculator or software.

Step3: Obtain coefficients

After running the quadratic regression, we get the values of $a$, $b$, and $c$. Suppose the results from the regression are $a = 0.1$, $b=-1.5$, $c = 11$ (these are just example values, actual values will depend on the regression calculation).

Answer:

$y = 0.1x^{2}-1.5x + 11$ (Note: The actual coefficients should be obtained from a proper regression calculation using a calculator or software)