To determine the quadratic function that best models the given set of data, we need to identify the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] of the quadratic equation in the form [tex]\( y = ax^2 + bx + c \)[/tex].
After analyzing the provided data and performing polynomial regression, the coefficients are found as follows:
- [tex]\( a = 0.14015151515151508 \)[/tex]
- [tex]\( b = -1.4265151515151515 \)[/tex]
- [tex]\( c = 10.75 \)[/tex]
Thus, the quadratic function that models the given set of data is:
[tex]\[ y = 0.14015151515151508 x^2 - 1.4265151515151515 x + 10.75 \][/tex]
