What’s the same and what’s different about the following pairs of equations?

  1. \(y=x^2-4\) and \(y+x^2-4=0\)

  2. \(y=4-9x^2\) and \(y+4=9x^2\)

  3. \(2y=4x^2-6\) and \(-(y-3)=2x^2\)

If you were given the following picture, could you suggest the equation of its pair?

Quadratic curve passing through x = plus or minus 2 root 3 and y = minus 12

How about if you were given this picture instead? Could you give the equation of its pair?

A quadratic curve tilted to the side that passes through x = minus 1 and y = plus or minus one third