Consider the table below. x    y -3  0.5 -2  1 -1  2.5 0  5 1  8.5 y=ax2+bx complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.

The standard equation is:
 y = ax2 + bx + c
 For this case, what we need to do is to evaluate three points in the standard equation and solve the system of three equations with three unknowns.
 We have then:
 For (-3, 0.5):
 0.5 = 9a - 3b + c
 For (0, 5):
 5 = c
 For (1, 8.5):
 8.5 = a + b + c
 We solve the system:
 0.5 = 9a - 3b + c
 8.5 = a + b + c
 5 = c
 From here we get:
 a = 1/2
 b = 3
 c = 5
 The standard equation is:
 y = (1/2) x ^ 2 + 3x + 5
 
 y = (1/2) x ^ 2 + 3x + 5