The graph of the given functions is shown below:
the blue curve is g(x) and the red line is f(x). Take into account that the solution to the system are the intersection points.
The points of the parabola can be found as follow:
the vertex of the parabollar (in this case, the minimum of g(x)) is given by:
x = -b/2a
where a=1 and b=2 (coefficient of the function). Then:
x = -2/2(1) = -1
then, for x=-1 there is the vertex of the function. By replacing the previous value into g(x):
g(2) = (1)^2 + 2(-1) - 8 = 1 - 2 - 8 = -9
Hence, the vertex of the parabolla is at (-1,-9)
other point of the parabolla is, for instance, the y-intercept. By making x=0, you obtain:
g(0) = 0^2 - 2*0 - 8 = -8
Hence, the y-intercept is the point (0,-8)
As you can notice the intersection points are (-3,-5) and (3,7)