Explanation for Question 27 From the Math (Calc) Section on the 2018 March Sat
Question 27 says the graph, 2 the equation above in the X, Y plane is a parabola, 3 which of the following equivalent forms of the equation includes the X and Y 4 coordinates of the vertex as constants. 5 So the first thing I'm going to do here is I'm going to factor 6 this equation so that I can find the zeros and 7 it becomes X minus eight X plus two, 8 which tells us that our zeros are X is equal to eight, 9 and X is equal to negative two. 10 Since parabolas are symmetrical about their vertex, 11 we can use these two zeros and find the midpoint, 12 and we know that that's going to be the vertex. And the midpoint is 13 X is equal to three. Finally, 14 we can plug in three into the equation to see what the Y value 15 is at the vertex. 16 So Y is equal to three squared plus negative six 17 times three plus negative 16. 18 This becomes Y is equal to nine plus negative 18 plus 19 negative 16, which is just equal to Y is equal to negative 20 25. And the equation out of these answer choices that has 21 negative 25 and positive three in it as Constance is 22 so a is the correct answer.