For a quadratic in standard form ax^2 + bx + c, the axis of symmetry is:

For a quadratic in standard form ax^2 + bx + c, the axis of symmetry is:

• A. x = -a/(2b)
• B. x = -b/(2a)
• C. x = b/(2a)
• D. x = -2a/b

Answer: (B)

The axis of symmetry for a parabola is the vertical line that passes through its vertex. For the quadratic y = ax^2 + bx + c, you can see this by completing the square: y = a[x^2 + (b/a)x] + c = a[(x + b/(2a))^2 - (b/(2a))^2] + c = a(x + b/(2a))^2 + [c - b^2/(4a)] The vertex occurs where the squared term is zero, which is at x = -b/(2a). Since the axis of symmetry is the vertical line through the vertex, it is x = -b/(2a). The other expressions don’t equal this x-coordinate in general, so they don’t describe the symmetry line.

The axis of symmetry for a parabola is the vertical line that passes through its vertex. For the quadratic y = ax^2 + bx + c, you can see this by completing the square:

y = a[x^2 + (b/a)x] + c

= a[(x + b/(2a))^2 - (b/(2a))^2] + c

= a(x + b/(2a))^2 + [c - b^2/(4a)]

The vertex occurs where the squared term is zero, which is at x = -b/(2a). Since the axis of symmetry is the vertical line through the vertex, it is x = -b/(2a). The other expressions don’t equal this x-coordinate in general, so they don’t describe the symmetry line.