Explanation for Question 38 From the Math (Calc) Section on the 2017 May Sat
Christian 38 is still relating to our scatterplot and our graph, 2 um, from the same ones as questions, 3 37. So just to review, 4 we know that the actual line, 5 so the parabola here is the model and then the actual 6 points are the real points. 7 Those are the scatterplot aspects of it. 8 They're the actual values. So question 38 says the quadratic model predicts 9 the average fuel economy to be 26 miles per gallon for how many different 10 speeds. Since we're talking about the quadratic model, 11 we know that we're going to be talking about the parabola, not the little 12 points. Now we want to know when the parabola is equal to, 13 um, 26 miles per hour. 14 So the average fuel economy we know is the y-axis. 15 So we look for 26, which is right here. 16 Now, whenever the graph, 17 the parabola crosses by the number 26, 18 that's when it's predicting that the average fuel economy will be 26. 19 So we can draw a line kind of on the 26th. 20 And we see that the parabola touches at twice at this point right here 21 and at this point right here. So those would be the two times that 22 the model predicts the average for the economy to be 26 miles 23 per gallon. So our answer would be two.
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