The curve with equation y = x² – 2x – 3 , where b and c are positive real numbers, crosses the x-axis at A and B, and the y-axis at C.

If you draw the circle that goes through all the points A, B and C, what are the co-ordinates of the other point where it crosses one of the axes?

What about the curve with equation y = x² – x – 3? Or y = x² – 3x – 3?

Can you generalise for curves of the form y = x² – bx – c, where b and c are positive real numbers?