[Video] Q30: Which of the following is an equivalent form of the equation of the graph shown in the xy-plane above, from which the coordinates of vertex a can be identified as constants in the equation?

Explanation for Question 30 From the Math (Calc) Section on the Official Sat Practice Test 1

No question number 30 is asking us, which of the following is equivalent and 2 from which the is vertex a can be identified as constants in the equation. 3 So what we're really looking for here is vertex form. 4 Right? What we can notice is that we have two zeros, 5 we have zero negative three. We have a zero at positive five. 6 And so this is true right here, 7 right? This negative three positive five. 8 Um, there's nothing wrong with that. That's right. 9 But it doesn't show us how to find the vertex. 10 So if you chose answer a, you did choose a correct equation, 11 but we needed to be able to identify the coordinates of the vertex. 12 So that's why a isn't going to work here. Now. 13 B is actually incorrect, right? We have the incorrect, 14 um, factors here because we didn't flip the signs of the zeros. 15 If we have a zero negative three, then our factor is plus three, 16 not minus three. 17 Now, if you said C um, 18 you got closer here, right? 19 But what we need to know is what our vertex is. 20 Now, our vertex is negative one, 21 common, negative 15, or it looks like actually negative 16. 22 And so we see here and see is negative two, 23 not negative one. So this C is not actually showing us the correct vertex, 24 right? It's giving us different numbers. Now D is 25 in vertex form, which is something that you learn in algebra two. 26 You usually, so you might recognize this, but it's basically X minus, 27 um, H squared minus K, 28 where H is the X coordinate of your vertex. 29 And then K is the Y coordinate of our vertex. 30 So we can see we've done here is actually, 31 should be plus K as we've subtracted, 32 the one which was our X coordinate of the vertex. 33 And then we've subtracted the 16, 34 which was the Y coordinate of our vertex. So D is written correctly in 35 for text form. It allows us to determine the vertex as our best answer, 36 then has to be de.