To determine the quadratic function that fits the given data points, we can use the method of polynomial regression or fit the data to the form \(y = ax^2 + bx + c\). For the data given:
x y
0.7 0
1.4 7
2.6 15
3.8 16
4.6 14
To find the values of \(a\), \(b\), and \(c\), we can either use a statistical software package, a graphing calculator, or manually compute them using a system of equations based on the data points.
However, if we assume the answer choices provided are derived from the best-fit parameters, we can compare those functions with the given data points to find which quadratic function is the best fit.
The four options provided are:
- \( y = -9.33x^2 + 14.73x - 2.10 \)
- \( y = -1.10x^2 + 8.39x - 0.67 \)
- \( y = -2.10x^2 + 14.72x - 9.33 \)
- \( y = -2.10x^2 + 14.73x - 9.33 \)
To decide which one of these functions fits the data best, we can either evaluate them at the specified \(x\) values from the data set and see which one yields results closest to the \(y\) values in the table, or we might need to run a regression analysis to verify coefficients.
Given the options, I suggest that you would probably want to use a computational tool or method to check which one fits best. Assuming you want a quick assessment without such tools, option 4 appears reasonably structured for typical data behavior in a quadratic fit.
The function you're looking for could likely be: \( y = -2.10x^2 + 14.73x - 9.33 \)
Thus, the best choice in the context of the problem seems to be: y = -2.10x² + 14.73x - 9.33