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)=x^2-3x+1 . Write a rule for g .

Answer 1

f(x) = x^2 -3x + 1 = (x-3/2)^2 + 13/4

stretched by factor of 3

y= 3(x-3/2)^2 + 13/4 has vertex (3/2, 13/4)

reflect over y axis, vertex becomes (-3/2, 13/4)

y = 3(x+3/2)^2 + 13/4

shift 2 units left, by increasing x by 2

g(x) = 3(x+7/2)^2 +13/4