Verified answer

[tex]y = {x}^{2} + x + 1[/tex]

[tex]x = - 3[/tex]

[tex]y = ( - 3) {}^{2} + ( - 3) + 1 = 9 -3 + 1 = 10 - 3 = 7[/tex]

[tex]x = - 2[/tex]

[tex]y = ( - 2) {}^{2} + ( - 2) + 1 = 4 - 2 + 1 = 5 - 2 = 3[/tex]

[tex]x = - 1[/tex]

[tex]y = ( - 1) {}^{2} + ( - 1) + 1 = 1 - 1 + 1 = 1[/tex]

[tex]x = 0[/tex]

[tex]y = 0 {}^{2} + 0+ 1 = 1[/tex]

[tex]x = 1[/tex]

[tex]y = {1}^{2} + 1 + 1 = 1 + 2 = 3[/tex]

[tex]x = 2[/tex]

[tex]y = 2 {}^{2} + 2 + 1 = 4 + 3 = 7[/tex]

[tex]x = 4[/tex]

[tex]y = {4}^{2} + 4 + 1 = 16 + 5 = 21[/tex]

[tex]x = 7[/tex]

[tex]y = 7 {}^{2} + 7 + 1 = 49 + 8 = 57[/tex]