If y=(15-6x2)/2, the parent function is y=x2, because it has the same degree (highest power of the variable). The function is a parabola and all parabolas have similar appearance. The other numbers (constants) in the given function shift the shape up and down and side to side, but the general shape is still a parabola.
The minus sign in front of the squared term inverts the usual U-shape of the parabola, that is, it's reflected in the x-axis. The coefficient 6/2=3 makes the parabola narrower (the arms are closer together). The remaining constant 15/2=7.5 lifts the inverted parabola, so the vertex moves from the origin (0,0) to (0,7.5). The parabola still has the same axis of symmetry (the y-axis).
When you're asked to find the parent function just look for the most basic (simplest) function which produce a graph of similar shape. Common shapes are straight lines, circles, ellipses, hyperbolas, parabolas.