Explanation for Question 11 From the Math (No Calc) Section on the Official Sat Practice Test 6
Question 11 gives us this graph and then it asks us the vertex of 2 the pull-up parabola and the X, Y plane above zero. 3 See, which of the following is true about the parabola with the equation? 4 Y equals negative a X minus B squared plus C. 5 All right. So sure enough, we can look at this graph and we know 6 that this graph is Y equals X squared, 7 plus C two things to note sure enough, 8 that vertex is at zero comma C, 9 as it says in the problem statement. And we can see that a must 10 be a positive constant, because the graph is curving upward. 11 And we know that because this positive, 12 constant, and it curving upward means that as X increases Y increases, 13 and that AA essentially defines the rate of growth of the parabola. 14 So how quickly it grows if it were to be a smaller number of 15 micro less quickly, so like this and so forth. 16 So knowing that a positive aim means that the graph curves upward, 17 we can infer that in this equation, we've got a negative eight. 18 So our graph probably opens downward. 19 So let's cross out a and C as potential answer choices. 20 Now we're left to choose, which are where the vertex is. 21 And we can see that sure enough, the Y coordinate is going to be 22 C again, because of that plus C right here. 23 And then we can infer that the X coordinate is going to be defined 24 by this part of the expression. The correct answer here is going to be 25 B comma C. And that's because if you think about this X minus 26 B equals zero, and kind of defining what the problem means you would get 27 X equals positive B. So for that reason, 28 the X coordinate is B the Y coordinate is C and the graph opens 29 downward. So you can pick B as your answer choice.