Final Answer:
The values of b that result in the function f(x) = x^2 + bx - 27 having a minimum value of -63 are b = -12 and b = 12.
Step-by-step explanation:
Given function f(x) = x^2 + bx - 27.
Identify the coefficient of the quadratic term (x^2) as 1.
Use the formula for the minimum value of a quadratic function f(x) = ax^2 + bx + c: Minimum value = c - (b^2 / 4a).
Substitute the given minimum value (-63) into the formula: -63 = -27 - (b^2 / 4).
Solve for b^2: b^2 = 144.
Find b: b = ±12.
Therefore, the values of b are -12 and 12, which satisfy the given conditions.