A is obviously wrong. The opening of the function image is downward, so the quadratic term coefficient is less than zero.

Substitute point (-1, 0) and point (2, 0) into three analytical expressions of b, c and d respectively, and option c does not meet the requirements.

b、y=- 1/2x？ + 1/2x+ 1

=- 1/2(x？ +x)+ 1

=- 1/2(x？ +x+ 1/4)+ 1/8+ 1

=- 1/2(x+ 1/2)？ +9/8

After the analytic formula of option B is converted into a vertex, the symmetry axis can be obtained as x=- 1/2, while the actual image symmetry axis is 2-2-(- 1)÷2= 1/2.

So option b doesn't match either

Look at option D again, the opening is downward, and the points (-1, 0) and (2,0) are substituted into the analytical formula, which meets the requirements.

y=-x？ +x+2

=-(x？ -x)+2

=-(x？ -x+ 1/4)+2+ 1/4

=-(x- 1/2)？ +9/4

The symmetry axis is x= 1/2, which meets the requirements.