Explanation for Question 15 From the Math (No Calc) Section on the 2019 October Sat
Not for number 15. The first thing that we should notice is that our 2 answer choices are written in what we call a vertex form. 3 And the general form of vertex form is Y is equal to a 4 times X minus H squared plus K, 5 where H is, um, the X coordinate of your vertex and K is 6 the Y coordinate of your vertex. So, 7 one thing that's important to notice is that whatever is on the inside here, 8 that H has the opposite sign of what is actually in your vertex. 9 So a good first point here is actually to look at the letter a, 10 the variable a and we should notice immediately that this parabola opens 11 downward. And when you have a parabola that opens downward, 12 that means you have a negative a value. 13 Whereas if you have a parabola that opens upward, 14 the first number that you see, the value is a positive value. 15 And so since this is a downward parabola, we know that our EI has 16 to be negative, which allows us to eliminate answer choice D and 17 now from our remaining answer choices, we can determine which is right, 18 and which ones are wrong by looking at the vertex. 19 And the vertex of our parabola is going to be somewhere around here. 20 And if we were to draw a line down from there onto the x-axis 21 and onto the y-axis, we would see that our vertex is at about 55 22 comma 50. So that means that we're going to want, 23 um, our H here to be a negative 55, 24 which is what we see in answer choice B and our K here to 25 be a positive 50, which is also what we see in answer choice B. 26 And so overall answer choice B is going to be the correct answer because 27 it shows the correct vertex with the correct H and K, 28 and then it also has the right a value being negative.