Question

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 8.5 9 what quadratic function best models this set of data? y = x² + x + -1.14 1.14 0.14 reset next

Explanation:

Step1: Recall quadratic regression formula

The general 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 coefficients $a$, $b$, and $c$ for the best - fit quadratic model. Input the year values as the $x$ - values ($x = 1,2,\cdots,9$) and the number of students (in thousands) as the $y$ - values.

Step2: Perform quadratic regression

Using a calculator or software for quadratic regression on the data points $(1,9.5),(2,8),(3,8.5),(4,7.5),(5,6.5),(6,6.5),(7,8.5),(8,8.5),(9,9)$, we get the quadratic function $y=-0.14x^{2}+1.71x + 7.93$ (rounded to two decimal places). So the coefficient of $x^{2}$ is $a=-0.14$.

Answer:

$y=- 0.14x^{2}+1.71x + 7.93$ (the first blank should be filled with $-0.14$)