Explanation for Question 13 From the Math (No Calc) Section on the 2017 October Sat
Question 13 says the graph of the function F in the X, 2 Y plane above is a parabola, 3 which of the following defines F. 4 So to find the equation of a parabola, 5 we're going to use this formula a times X minus H squared plus 6 K, where HK is the coordinates of the vertex. 7 So the first thing we're going to do is we're going to find the 8 vertex of the problem, and we're going to plug those numbers into this equation. 9 So as you can see, the vertex is at three one, 10 which means that this equation should be rewritten as X minus three 11 squared plus one. 12 And from that, we can already eliminate answer choices, 13 B and D, but we still need to solve for the value of X. 14 And the way we're going to do that is by plugging in a coordinate 15 from the parabola. That's not the vertex. 16 So any point we're just going to take two, 17 five. So we know that F of X is equal to a times X 18 minus three squared plus one. So we can rewrite that as five is equal 19 to a times two minus three squared, 20 plus one, and use this to sell for a, 21 we can rewrite this as five is equal to a times, 22 negative one squared. Plus one, 23 we know that negative one squared is just positive one. 24 So this can be rewritten as a plus one, 25 we can subtract one from both sides. And that tells us that a 26 is equal to four, which means that our final equation should be four times 27 X minus three squared plus one, 28 which is answer choice.