The graph of function f(x) and the graph of function g(x) meet at two different points. What is the value of a?

g(x) = -x^{2} + a

Solution:

The two functions have a solution in the third quadrant, regardless of the value of *a*.

In quadrant 1, for different values of *a*, the two functions have 0, 1 or 2 points of intersection. In order to have only one point of intersection in this quadrant,
the functions have to be tangent. This means that:

x = 2.

f(2) = g(2)

a = 12