[Video] Q35: The graph of the function f, defined by f(x) = -1/2(x-4)^2 + 10, is shown in the xy-plane above. if the function g (not shown) is defined by g(x) -x + 10, what is one possible value of a such that f(a)= g(a) ?

Explanation for Question 35 From the Math (Calc) Section on the Official Sat Practice Test 8

So the question 35 gives us the graph of this function here F of 2 X. And it's asking us where FFA is equal to GFA in 3 reality, what this means is that they're just asking for where these two graphs 4 intersect. And we know this because a is 5 where we would normally see an X, right? 6 And so what we're looking at is at what point on the X axis, 7 do these two lines have the same Y value, 8 which connotates that they're in intersecting with each other. 9 And so maybe the easiest way to do this is to take this line 10 negative X plus 10, and graph it onto this graph and see where the 11 lines cross. So we know that for G of X, 12 we have a Y intercept at 10, and then from there we have a 13 slope of negative one. So we need to go down one and over one. 14 And so it's possible that one place you could have gotten tripped up on 15 this, on this question, is that rather than going down one box over one 16 box, we actually need to go down one box over two boxes because we 17 can see here that moving over one is actually moving over two boxes. 18 So our points are going to be these instead, 19 and we can draw a line through them just like that. 20 And we see that the two points at which we intersect are going to 21 be when X is equal to eight and when X is equal to two. 22 So our possible answers, you only had to say one, 23 but there were two possibilities are either eight or to.

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