Find a quadratic equation whose graph has each of the following characteristics:

1. No $x$-intercepts and a negative $y$-intercept.

   Hint (a):

   Write the equation of an inverted parabola with a vertex below the x-axis.

2. One $x$-intercept and a positive $y$-intercept.

   Hint (b):

   This parabola will sit on the x-axis.

3. Two x-intercepts and a negative y-intercept.

   Hint (c):

   Shift the graph of $y = x²$ down.