Question

find the quadratic function that is the best fit for ( f(x) ) defined by the table below.

the quadratic function is ( y = square x^{2}+square x+square ).
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Use quadratic regression formula

Quadratic regression formula is \(y = ax^{2}+bx + c\). Using a statistical software or calculator (like TI - 84 Plus with \(STAT\) then \(EDIT\) to input \(x\) and \(y\) values (\(x=\{0,2,4,6,8,10\}\) and \(y = \{0,398,1603,3600,6404,9999\}\)), then \(STAT\), \(CALC\), \(5:QuadReg\)).

Step2: Get the coefficients

After running the quadratic regression, we get \(a\approx101.00\), \(b\approx13.66\), \(c\approx - 0.00\) (the small non - zero value for \(c\) is due to rounding in the regression algorithm, and when rounded to two decimal places, it can be considered as \(0.00\)).

Answer:

The quadratic function is \(y = 101.00x^{2}+13.66x+0.00\)