To find the quadratic function that best models this data set, we follow these steps:
1. Identify the form of the quadratic equation: [tex]\( y = ax^2 + bx + c \)[/tex].
2. Using statistical methods to fit a quadratic model to the given data points representing the years (x) and the number of students (y), we find the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
3. The result from the fitting process provides the coefficients:
- [tex]\( a = 0.140 \)[/tex]
- [tex]\( b = -1.427 \)[/tex]
- [tex]\( c = 10.75 \)[/tex]
Therefore, the quadratic function that best models the set of data is:
[tex]\[ y = 0.140x^2 - 1.427x + 10.75 \][/tex]
Now, fill in the blanks in the quadratic function:
[tex]\[ y = \boxed{0.140}x^2 + \boxed{-1.427}x + \boxed{10.75} \][/tex]
