Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f(x)=x2−x+1. Write a rule for g. g(x)=

Answer 1

stretch vertically by a factor of 3: 3x^2-3x+3

reflection in y-axis: 3(-x)^2 -3(-x) + 3 = 3x^2 + 3x + 3

translation to the left: 3(x+2)^2 + 3(x+2) + 3 = 3(x^2 + 4x + 4) + 3x + 6 + 3 = 3x^2 + 12x + 12 +3x + 6 + 3 = 3x^2 + 15x + 21