The quadratic ax^2 + bx + c can be expressed in the form 2(x - 4)^2 + 8. When the quadratic 3ax^2 + 3bx + 3c is expressed in the form n(x - h)^2 + k, what is h?
+128475 2(x - 4)^2 + 8 =
2 (x^2 - 8x + 16) + 8 =
2x^2 - 16x + 32 + 8 =
2x^2 - 16x + 40 so........a = 2, b = -16 and c = 40
So....3ax^2 +3bx + c = 3(2)x^2 + 3(-16)x + 40 = 6x^2 - 48x + 40
Factor out the 6 and we have
6 ( x^2 - 8x + 40/6 ) T
Take 1/2 of - 8 = - 4.....square this = 16 and add and subtract within the parentheses
6 ( x^2 - 8x + 16 + 40/6 - 16) factor the first three terms and simplify the rest
6 [ (x - 4)^2 + 20/3 -48/3 ]
6 [ ( x - 4)^2 - 28/3 ]
6 ( x - 4)^2 - 56
So h = 4
