Question

Which set of systems of equations represents the solution to the graph?an upward opening parabola decreasing from negative 3 comma 8 to a minimum at negative 1 comma 4 and then increasing to 1 comma 8 and a downward opening parabola increasing from negative 2 comma 1 to a maximum at 0 comma 5 and then decreasing through the point 1 comma 4A. f(x) = –x2 + 2x + 5g(x) = x2 + 5B. f(x) = –x2 + 2x – 5g(x) = x2 + 5C. f(x) = x2 + 2x – 5g(x) = –x2 + 5D. f(x) = x2 + 2x + 5g(x) = –x2 + 5

Answer 1

Looking at the graph we can identify both functions have a y-intercept of y = 5. This would be the independent term of both parabolas, so choices B and C are discarded because one of the functions in each choice has a y-intercept of -5.

This gives only two valid choices: A and D.

We can also see the parabola that is symmetrical with respect to the y-axis (the red one) is concave down, so its leading coefficient must be negative.

The condition above only occurs in choice D, so it's our correct answer:

D