To find the axis of symmetry of a parabola given by y = ax^2 + bx + c, use the formula for the x-coordinate of the vertex: x = -b/(2a).
Here a = 1 and b = 2, so
x = -b/(2a) = -2/(2·1) = -1.
We can confirm by completing the square:
y = x^2 + 2x + 47/5 = (x^2 + 2x + 1) + 47/5 - 1 = (x + 1)^2 + (47/5 - 5/5) = (x + 1)^2 + 42/5.
The vertex is at (−1, 42/5), so the axis of symmetry is the vertical line x = −1.
Answer: x = -1