Explanation for Question 36 From the Math (Calc) Section on the 2019 April Sat
And 36, we were told that the graph of Y equals X squared plus 2 BX, plus C has X intercepts at X equals negative two and X equals 3 negative six. And we are looking for the value of beat. 4 So usually we would take a polynomial and factor it, 5 then set each factor equal to zero to find the X intercepts. 6 But this time we are given the X intercepts and we are going to 7 use those to work backwards and find the factored form. 8 So if the X intercepts are at X equals negative two and X 9 equals negative six, then if we add two to both sides, 10 X plus two is equal to zero, 11 and this would be what we would do. If X plus two is a 12 factor in order to find the X intercept. 13 So using the same logic, we're going to have X plus six equals zero. 14 So that means our factored form is X plus two X 15 plus six. You can also just take these X intercepts and 16 flip the signs, and those will be the signs that you use in the 17 factors. So now that we have our factor form, 18 we can go ahead and foil it in order to get it, 19 to match this form up here. So we have X times X 20 is X squared, X times six is six X, 21 two times X is two X and two times six is 12. 22 Now we can combine like terms and get I'm going to rewrite it up 23 here. X squared plus eight X plus 12. 24 So now comparing to our original equation here B 25 is equal to eight. So the answer to number 36 is eight.