Solution:

Given function: p(x) = x^2 - 4x + 3

To evaluate p(2) - p(-1) and p(1/2), we need to substitute the given values into the function and perform the necessary calculations.

1. Evaluating p(2):
- Substitute x = 2 into the function: p(2) = (2)^2 - 4(2) + 3
- Simplify the expression: p(2) = 4 - 8 + 3 = -1

2. Evaluating p(-1):
- Substitute x = -1 into the function: p(-1) = (-1)^2 - 4(-1) + 3
- Simplify the expression: p(-1) = 1 + 4 + 3 = 8

3. Evaluating p(1/2):
- Substitute x = 1/2 into the function: p(1/2) = (1/2)^2 - 4(1/2) + 3
- Simplify the expression: p(1/2) = 1/4 - 2 + 3 = 5/4

Now, let's calculate the final results:

p(2) - p(-1) = (-1) - 8 = -9

p(1/2) = 5/4

Therefore, p(2) - p(-1) = -9 and p(1/2) = 5/4.

Summary:
- p(2) - p(-1) = -9
- p(1/2) = 5/4

By substituting the given values into the function and performing the necessary calculations, we have evaluated p(2)-p(-1) and p(1/2) as -9 and 5/4, respectively.