Explanation for Question 12 From the Math (No Calc) Section on the 2018 April Sat
Question 12 says the graph of function F is shown in the X, 2 Y plane above where Y is equal to F of X, 3 which of the following functions could define F. 4 So when you're trying to find the equation of these types of graphs, 5 all you have to do is figure out what the zeros of the graphs 6 are. So for example, 7 we know that there's a zero at negative three because that's where the graph 8 passes through the X axis. 9 So Y is equal to zero at that point, 10 which means that we know that part of this graphs equation is going to 11 be X plus three. 12 And that's because whatever the zero is the gonna plug in, 13 like I've written up here as K. 14 So since our zero is negative three, 15 uh, I plugged that into as K and this became X minus negative three 16 or X plus three. 17 We also know that there's a zero at negative one. 18 So we know that we also should write out X plus one as part 19 of this equation. However, 20 this zero is a little bit different than the first zero. 21 And that's because it doesn't go through the x-axis, 22 but instead it balances off of it. 23 And whenever you have a zero that bounces off the x-axis, 24 you want to square whatever that factor is. 25 And then finally, our last zero is positive two. 26 So we know X minus two squared should be the last 27 part of our equation because this bounces off the x-axis. 28 And so we know that the correct answer is X plus three X plus 29 one squared X minus two squared, 30 and that's answer choice C.