It looks like you've written the same equation twice:

\[ y = \frac{1}{2}x^2 + 1 \]

This is a quadratic equation in the form of \( y = ax^2 + bx + c \), where \( a = \frac{1}{2} \), \( b = 0 \), and \( c = 1 \).

This equation represents a parabola that opens upwards since the coefficient of \( x^2 \) (which is \(\frac{1}{2}\)) is positive. The vertex of this parabola is located at the point (0, 1), which can be derived from the general vertex form of a parabola. There is no linear term, meaning that the axis of symmetry is the y-axis. If you have any specific questions about this equation or need further assistance with related problems, feel free to ask!