Suneung CSAT Algebra Problem

 




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) = -x2 + 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