The quadratic ax^2 + bx + c can be expressed in the form 2(x - 8)^2 + 4. When the quadratic 3ax^2 + 2bx + c is expressed in the form n(x - h)^2 + k, what is h?
+130071 2(x - 8)^2 + 4 =
2 (x^2 - 16x + 64) + 4 =
2x^2 - 32x + 128 + 4 =
2x^2 -32x + 132
a = 2
b = -32
c = 132
So
3ax^2 + 2bx + c =
6x^2- 64x + 132
6 [ x^2 - (32/3)x + 22] complete the square on the terms in the brackets
Note : ([ 32/3] [1/2]) = (16/3)^2 =256/9
6 [ x^2 - (32/3)x + 256/9 + 22 - 266/9 ] =
6 [ (x - (16/3)]^2 + 6 [ -58/9] =
6 [ x - (16/3) ]^2 -116/3
h = 16/3
