SAT Math Multiple Choice Practice Question 460: Answer and Explanation
The graph of y = g(x) is shown in the figure above. If g(x) = ax2 + bx + c for constants a, b, and c, and if abc ≠ 0, then which of the following must be true?
A. ac > 1
B. c > 1
C. ac < 0
D. a > 0
E. ac > 0
Correct Answer: E
E Remember your transformation rules. Whenever a parabola faces down, the quadratic equation has a negative sign in front of it. It always helps to plug in! Let's take an example. If your original equation was (x + 2)2, putting a negative sign in front, –(x + 2)2, would flip the parabola. If you expand out that equation, you get –x2 – 4x – 4. Notice that a in this equation is –1. Also, notice that c in the equation is just the y-intercept, because if you plug in 0 for x you get y = c. On the graph, the y-intercept is negative. And a negative number times a negative number is always positive. Again, plug in if you like it better: (–1)(–4) = +4. The best answer is E.