If we have a y intercept of 8, then the point (0,8) must be on the graph
We have this
8 = a(0 + 3/2)^2 + 7/4
8 = a(9/4) + 7/4
32 = 9a + 7
25 = 9a
a = 25/9
So we have
y = (25/9)(x + 3/2)^2 + 7/4
Look at the graph here https://www.desmos.com/calculator/jdr4rgp3vj
Note that none of the given answers are correct......