To find the quadratic function that best models the given set of data, we fit a quadratic function to the provided enrollment numbers. The form of the quadratic function is [tex]\( y = ax^2 + bx + c \)[/tex].
1. The data points we have are:
- Year (x): 1, 2, 3, 4, 5, 6, 7, 8, 9
- Students (y): 9.5, 8, 8.5, 7.5, 6.5, 6.5, 8.5, 8.5, 9
2. By finding the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] of the quadratic function that best fits this data, we obtain:
- [tex]\( a = 0.14015151515151508 \)[/tex]
- [tex]\( b = -1.4265151515151515 \)[/tex]
- [tex]\( c = 10.75 \)[/tex]
Therefore, the quadratic function that best models this set of data is:
[tex]\[ y = 0.14015151515151508 \cdot x^2 - 1.4265151515151515 \cdot x + 10.75 \][/tex]
So when filling in the blanks, you should have:
[tex]\[ y = \boxed{0.14015151515151508} x^2 + \boxed{-1.4265151515151515} x + \boxed{10.75} \][/tex]
