Y=ax^2 + bx + c1. 9 = a*3^2 + b*3 +c 2. 25 = a*5^2 + b*5 +c3. 4 = a*(-2)^2 + b*(-2) + c -------------------------------Let's make the equations more simple: 1. 9 = 9a + 3b + c 2. 25 = 25a + 5b + c3. 4 = 4a -2b + c--------------------------------Let's reduce the number of equations to 2. We'll do it as follows: From equation no. 3 we see that c = -4a +2b +4 Now we shall put that value instead of c in the other 2 equations: 1. 9 = 9a + 3b -4a +2b +4 that will make: 5 = 5a +5b or 1 = a +b (getting simple, hey ?)2. 25 = 25a + 5b -4a +2b +4 that will make: 21 = 21a + 7B or (divide by 7) 3 = 3a + b--------------------------------------Now: from 1 = a + b we get a = 1-b Let us install it in equation no. 2 to get:3 = 3 (1 - b) + b3 = 3 - 3b +b 0 = -2b that means b = 0 Since a = 1 -b and b=0 that means a= 1Now go back c = -4a +2b +4 or c = -4 + 4 c = 0So the equation looks as follows: Y = X^2
OronD has said it all
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