Determine at what value of a the axis of the parabola y = x ^ 2 + 2ax + a ^ 2 + b has the equation x = -1?

Solution:

1. The axis of the parabola y = Ax ^ 2 + Bx + C has the equation:
x = -B / 2A.

2. For the function y = x ^ 2 + 2ax + a ^ 2 + b we have:
A = 1; B = 2a; C = a ^ 2 + b.

Therefore, the axis of the parabola has the equation:
x = -B / 2A;
x = – 2a / 1;
x = -2a.

3. Therefore, the parabola y = x ^ 2 + 2ax + a ^ 2 + b will have the equation x = -1 provided:
-2a = -1;
a = 1/2.

Answer: 1/2.