Final answer:
The equation (x + 1)^2 typically represents a parabola, but the options provided don't fully align with the given equation since there is no information to determine if the parabola opens upwards or downwards.
Step-by-step explanation:
The equation provided is (x + 1)^2. This equation describes a parabola since it is in the form of x^2 (or (x - h)^2), which is characteristic of parabolas. However, the equation as written does not define the orientation or the position of the parabola regarding opening upwards or downwards, or about ellipses or circles.
Parabolas typically have an equation in the form of y = ax^2 + bx + c when they open upwards or downwards. For a parabola to open upwards, the coefficient 'a' must be positive, and for it to open downwards, 'a' must be negative. Circles and ellipses have equations with both x^2 and y^2 terms.
Hence, the correct answer to this question would be Parabola but the options provided are not fully consistent with the equation given. A complete quadratic equation in one variable, like (x + 1)^2, suggests a parabola that opens upwards or downwards depending on additional information, usually a 'y=' part, which is not provided here.