Explanation for Question 12 From the Math (No Calc) Section on the 2017 May Sat
Question 12 asks us, which of the following equations. 2 How's the graph and the X, Y plane with no X intercepts. 3 The important part here is understanding what it means to have no X intercepts, 4 a graph that has no X intercepts is simply just align that 5 never crosses the X axis. 6 So for example, this graph right here, 7 this line has no X intercepts. 8 You could also have a line like this. 9 This also never crosses the x-axis. So it doesn't have an X intercept when 10 it comes to an actual equation, 11 like the ones that they give us here and our answer choices, 12 how we figure out if a line has no X intercepts, 13 is that there's no solution for X one Y equals zero. 14 So the easiest way to go through this problem is just to go through 15 the equations and figure out which one, 16 um, has no solution. 17 One Y equals zero for a, 18 we have plugging zero for Y and we have zero equals 19 X squared, plus three X plus four to 20 solve for X. We need a factor. So we set up our two binomials. 21 We equal them to zero. We put in our exes and 22 we try and find two numbers that multiply to four and add 23 up to three. So we think of the factors of four and they are 24 one and four or two and two. 25 Now we also need them to auto to three. 26 We can cross out two and two immediately because there's no way that that 27 can add up to two, three. The one in four might make us doubt 28 ourselves a little bit, but the only way that we can make one in 29 four equal to three is if we...