Difficult Parabola Question for the SAT with Solution Let’s solve the parabola problem I posted on Wednesday. I’ll give the question one more time, followed by a solution. Level 5 Passport to Advanced Math The vertex of the parabola in the xy-plane above is (h, k). Which of the following is true about the parabola with the equation y = –ax2 + k ? A) The parabola opens upward and the vertex is (0, k). B) The parabola opens downward and the vertex is (0, k). C) The parabola opens upward and the vertex is (0, –k). D) The parabola opens downward and the vertex is (0, –k). Solution: From the given picture, we see that the graph of the given equation is an upward facing parabola. It follows that a > 0. Therefore, –a < 0, and the graph of y = –ax2 + k is a downward facing parabola. So, we can eliminate choices A and C. Now, the equation y = –ax2 + k can be written as y = –a(x – 0)2 + k. This is in standard form, and the graph of this equation is a parabola with vertex (0, k). So, the answer is choice B. Note: Here is a graph of both parabolas drawn on the same set of axes. Share this problem with your Facebook friends that are preparing for the SAT If you’re preparing for the SAT, you may want to check out the Get 800 collection of SAT math books. Comments comments