F(x) has exactly one intercept at the origin. g(x) is transformed from f(x) by flipping it (the minus sign at the x2) and then lifting it by 7 units. This means that the resulting mountain parabola will have two x-intercepts. Mathematically, a parabola has exactly one x-intercepts when its discriminant equals 0, it has 2 intercepts for D>0.
For g(x), a=-1, b=0 and c=7, so D=28, meaning 2 intercepts!
The function started facing up with a vertex at (0,0) since 7 was added before squaring , the graph shifts 7 units up so the vertex at (7,0) also , the function is negative do the graph is pointing down.
This means that there are two x- intercepts in g(x) and there was one x- intercepts in f(x).
