Which of these are quadratic equations? Give a reason for each.

Step 1. (a) $x^2 + 2x - 3 = 0$. Quadratic.

Step 2. (b) $x^2 - 2x + 1 = x^2 + 4$ gives $-2x - 3 = 0$. The $x^2$ terms cancel: linear, not quadratic.

Step 3. (c) $x^2 - 4 = 2x^2 - 1$ gives $-x^2 - 3 = 0$, that is $x^2 + 3 = 0$. Quadratic.

Step 4. (d) The $x^3$ terms cancel: $-x^2 - 5 = 0$, that is $x^2 + 5 = 0$. Quadratic.