Question

If p(x) = x² - 4x + 3, evaluate : p(2) - p(-1) + p(1/2)

A. 31/4
B. −31/2
C. −31/4
D. 31/2

Answer 1

To evaluate the function p(x) = x² - 4x + 3 at points 2, -1, and 1/2, we substitute and calculate to find that p(2) - p(-1) + p(1/2) is equal to -31/4.

Step-by-step explanation:

To evaluate p(2) - p(-1) + p(1/2) for the function p(x) = x² - 4x + 3, we need to substitute x with 2, -1, and 1/2 respectively in the function and calculate the values.

• For p(2): p(2) = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1.
• For p(-1): p(-1) = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8.
• For p(1/2): p(1/2) = (1/2)² - 4(1/2) + 3 = 1/4 - 2 + 3 = 1 + 1/4 = 5/4.

Now, combining these results we get: p(2) - p(-1) + p(1/2) = -1 - 8 + 5/4 = -9 + 5/4 = -36/4 + 5/4 = -31/4.

Therefore, the correct answer is C. −31/4.