Answer:

| $x$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | =45 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $y$ | 2 | 6 | 7 | 8 | 10 | 11 | 11 | 10 | 9 | =74 | | $xy$ | 2 | 12 | 21 | 32 | 50 | 66 | 77 | 80 | 81 | =421 | | $x^2y$ | 2 | 24 | 63 | 128 | 250 | 396 | 539 | 640 | 729 | =2771 | | $x^2$ | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | =285 | | $x^3$ | 1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 | 729 | =2025 | | $x^4$ | 1 | 16 | 81 | 256 | 625 | 1296 | 2401 | 4096 | 6561 | =15333 | Here normal equations are: $\sum y=9a_0+a_1\sum x+a_2 \sum x^2$ $\sum xy=a_0 \sum x+a_1\sum x^2+a_2 \sum x^3$ $\sum x^2y=a_0 \sum x^2+a_1\sum x^3+a_2 \sum x^4$ Thus, $74=9a_0+45a_1+285a_2$ $421=45a_0+285a_1+2025a_2$ $2771=285a_0+2025a_1+15333a_2$ Solving these equations, we get $a_0 =-\dfrac{13}{14}, a_1=\dfrac{16277}{4620}, a_2 =- \dfrac{247}{924}.$ Hence the parabolic curve is $y=a_0+a_1x+a_2x^2=-\dfrac{13}{14}+\dfrac{16277}{4620}x-\dfrac{247}{924}x^2.$                    Answer.