Q15

y = x²

y = -x² + 8x - 16
y = -(x² - 8x + 16)
y = - (x - 4)²

The first graph is a smiley face graph with a minimum point at (0, 0).

The second graph is a sad face graph with a maximum point at (4, 0).

These turning points occur at the same height level - the horizontal axis itself. The only way we can draw a common tangent is the horizontal axis itself. Any other tangent to any one of the curves will result in two intersection points with the other curve.

So, the sole common tangent is the horizontal axis.

For Q16, you have to make y the subject. When we take the square root for y, in this scenario we just take the positive square root because (1, 2) lies in the upper half of the entire coordinate board.