The values are:
- a = 0
- b = 0
- c = 12
- d = 20
This implies that the quadratic expression is y = (x + 2)(x + 1).
To determine the values of a, b, c, and d, we substitute the given values of x and y into the quadratic equation y = x^2 + 3x + 2.
1. For x = -2: a = (-2)^2 + 3(-2) + 2 = 4 - 6 + 2 = 0.
2. For x = -1: b = (-1)^2 + 3(-1) + 2 = 1 - 3 + 2 = 0.
3. For x = 2: c = (2)^2 + 3(2) + 2 = 4 + 6 + 2 = 12.
4. For x = 3: d = (3)^2 + 3(3) + 2 = 9 + 9 + 2 = 20.
The values are:
- a = 0
- b = 0
- c = 12
- d = 20
These results imply that the coefficients a and b are both zero, indicating that the quadratic expression y = x^2 + 3x + 2 can be factored as y = (x + 2)(x + 1). Therefore, when x = -2, x = -1, x = 2, and x = 3, the corresponding values of y are 0, 0, 12, and 20, respectively.