SAT Math Multiple Choice Practice Question 216: Answer and Explanation
The graph shown here is of y = ax2 + bx + c. Which of the following is a true statement?
A. a > 0 and c > 0
B. a < 0 and c < 0
C. a > 0 and c < 0
D. a < 0 and c > 0
E. a < 0 and c = 0
Correct Answer: D
D. Remember that if a in ax2 + bx + c is positive, the parabola will open upward (like a cup), and if a is negative, it will open downward (like a hill). This parabola opens downward, so you know that a is negative, and therefore a < 0; the right answer must be Choice (B), (D), or (E). The value of c turns out to be where the parabola intersects the y-axis (because on the y-axis the x-value is 0, so all the terms with x in them equal 0 too, leaving only c. The parabola shown clearly intersects the y--axis where it is positive, so c > 0. Choice (D) is your answer!