Final answer:
The axis of symmetry for the quadratic function f(x) = x^2 + 3 is x = 0 or the y-axis. It is found using the formula x = -b/(2a), but in this function, b = 0, thus the axis is the y-axis itself.
Step-by-step explanation:
The axis of symmetry of a parabola represented by a quadratic function of the form f(x) = ax^2 + bx + c is a vertical line that passes through the vertex of the parabola. The equation for the axis of symmetry can be derived from the quadratic equation by using the formula x = -b/(2a).
In the case of the function f(x) = x^2 + 3, given that there is no b term (which is effectively 0), the axis of symmetry is x = 0, which is the y-axis itself. This is because the vertex of the parabola occurs at the point where the first derivative of the function (which gives the slope) is zero, indicating a minimum or maximum point, which for a parabola will be its vertex.
The significance of the axis of symmetry is that it divides the parabola into two mirror images, reflecting that if you fold the parabola along this axis, both halves will match perfectly.