Questions: Find the quadratic function that models the data in the table below. x -2 -1 0 1 2 3 4 5 6 7 8 9 10 y 26 9 0 -1 6 21 44 75 114 161 216 279 350 The equation of the quadratic function that models the given data is y= x^2 + x + .

Solution Steps

The given data points are:

\[ \begin{array}{|c|c|} \hline \mathbf{x} & \mathbf{y} \\ \hline -2 & 26 \\ -1 & 9 \\ 0 & 0 \\ 1 & -1 \\ 2 & 6 \\ 3 & 21 \\ 4 & 44 \\ 5 & 75 \\ 6 & 114 \\ 7 & 161 \\ 8 & 216 \\ 9 & 279 \\ 10 & 350 \\ \hline \end{array} \]

Using quadratic regression, we find the quadratic function that models the data. The resulting equation is:

\[ y = 4.00x^2 - 5.00x - 0.00 \]

The coefficients of the quadratic equation are:

• \( a = 4.00 \)
• \( b = -5.00 \)
• \( c = -0.00 \)

This indicates that the parabola opens upwards (since \( a > 0 \)) and has its vertex at a point determined by the values of \( a \) and \( b \).

Final Answer