Question

Which set of systems of equations represents the solution to the graph?

an upward opening parabola decreasing from negative 3 comma 4 to a minimum at negative one comma zero and then increasing to 1 comma 4 and a downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3

f(x) = x2 + 2x + 1
g(x) = –x2 + 1
f(x) = x2 + 2x + 1
g(x) = –x2 – 1
f(x) = –x2 + 2x + 1
g(x) = x2 + 1
f(x) = –x2 + 2x + 1
g(x) = x2 – 1

Answer 1

The given graph consists of two parabolas. One is an upward opening parabola that decreases from (-3, 4) to a minimum at (-1, 0) and then increases to (1, 4). The equation of such a parabola is f(x) = -x^2 + 2x + 1. The other is a downward opening parabola that increases from (-2, -3) to a maximum at (0, 1) and then decreases through (2, -3). The equation of such a parabola is g(x) = x^2 + 1.

Therefore, the set of systems of equations that represents the solution to the graph is:

f(x) = -x^2 + 2x + 1

g(x) = x^2 + 1