SAT Math Problem (22)

Question

A portion of the graph of the quadratic equation described below y=f(x) is shownin the xy-plane above. The function g is defined by the equation g(x) = f(x) + b. If the equation g(x) = 0 has exactly one solution, what is the value of b?

 

y=f(x)

zeros: (-1,0) ; (3,0)

vertex: (1,-2)

 

Note: the original question included a graphic, but since I can't upload that graphic, I included the above points which were the only points given to me on the graphic anyway.

Answer 1

If the equation g(x) = 0 has exactly one solution, the the graph "sits" on the x-axis, i.e. the vertex of g(x) has y-coordinate = 0. Hence g(x) = f(x) + 2