Answer Choices
-9a
-8a
-5a
-2a
Explanation for Question 12 From the Math (No Calc) Section on the Official Sat Practice Test 3
Now for number 12, we're given a quadratic equation, 2 which makes a parabola, right? And so you'll see that they say a is 3 a non zero constant. The sat really likes to throw around that word constant. 4 It just means that a is a normal number, 5 like negative one, two or three. In this case, 6 it can't be zero, but sometimes it can be. Um, 7 and it's also always the same number. 8 So if a is negative one, it is always going to be negative one. 9 And then we're told that the vertex is CD, 10 right? So C is our X coordinate and D is our Y coordinate. 11 And so they basically want to know what is the Y coordinate of my 12 vertex, the best way to go about that for this particular problem is 13 going to be, to use the zeros that they gave us to find the 14 vertex. 15 And what's important to know is that parabolas are symmetric. 16 So what that means is that you'll always find your vertex, 17 always halfway between, 18 um, your two zeros. In this case, 19 our zeros are two, a negative four. So 2 1, 2, 3, 4, 20 negative four, and halfway between two and negative four by jump halfway 21 I'm I have an X of negative one, 22 right? So now I know what my X value is. 23 So I'll pull again that negative one and I'll get the Y value, 24 which is the right. So Y is equal to a times negative one minus 25 two, because that's the X of my vertex and negative one plus 26 four. So Y is equal to a Y 27 is equal to a times, 28 negative three times three, which is a, 29 a Y is equal to negative nine. Okay. 30 So depending on what AA is, you might find your vertex up here. 31 Um, if a was a negative number, 32 it would be up, but the bottom line is that your parabola might look 33 something like this, or it might look something like this, 34 but your vertex will have an X coordinate of negative one and a Y 35 coordinate of negative nine times a.