Explanation for Question 19 From the Math (Calc) Section on the 2020 March Sat
So number 19 gives us a quadratic equation and the forum that 2 it's factored in right in factored form and asks us what is a minimum 3 value would be. And so the best thing to do here is first to 4 think about this visually, right? Because we know that this parabola looks something 5 like this, right? It opens upwards because we have a positive out 6 here. We have two positives, so it doesn't have a negative coefficient. 7 So must open up and it has a value that is it's a lowest, 8 but how do we figure out where that value is? 9 Right. And we don't need to know the Y coordinate of it. We just 10 need to know the X coordinate of it. And so something that you can 11 think about here is that parabolas must have symmetry. 12 So if we can find where the two zeros are, 13 then we can go halfway between the two zeros and know that that is 14 where our minimum value has to be. We look at this, 15 we can say each of our set of parentheses equal to zero, 16 that way we can solve for where the zeros of our function are. 17 So if X minus five, our first print, this equal to zero, 18 I can add five to both sides. Now we'll get the X is equal 19 to five. So let me go ahead and draw a graph right here. 20 And if X is equal to 5 1, 2, 3, 4, 5, 21 then I have a zero right here, looks something like that at that point. 22 And then my other parenthesis says X plus five. 23 So I can set X plus five equal to zero, 24 and I can solve for X by subtracting five from both sides. 25 And I get the X i...