Write x^2+4x-12 in the form (x+a)^2+b where 'a' and 'b' are constants to be determined.
This question is asking us to complete the square. To find the value of a we must halve the coefficient of x. So, in this question: a = 4/2 = 2. To find the value of b we take the constant at the end of the quadratic, -12, in this case and subtract a2 from it: x2+4x-12 = (x+2)2-12-(2)2 - our value of a = 2, and 22 = 4 so: (x+2)2-12-4 = (x+2)2-16. So, a = 2, and b = -16. To check if these 2 quadratics are equal we can simply expand (x+2)2-16 to get: x2+2x+2x+4-16 = x2+4x-12 so we know we have completed the square correctly.
