Find the co-ordinates of the turning point of the line with equation y = x^2 + ax + b that passes through (1, 47) and (2, 60)
y = x2 + ax + bWhen x=1:47 = (1)2 + a(1) + b47 = 1 + a + b46 = a + bWhen x = 260 = (2)2 + a(2) + b60 = 4 + 2a + b56 = 2a + b Let this be equation 1Let 46 = a + b be equation 2Subtract equation 2 from equation 110 = aSubstitute a = 10 into equation 246 = 10 + b36 = bTherefore the equation of the line is y = x2 + 10x + 36y = x2 + 10x + 36 = (x+5)2+36-25 = (x+5)2+11Turning point has co-ordinates (-5,11)
