1. The problem statement, all variables and given/known data Let g(x) be the quadratic function: [tex] g(x) = (x - 1)^2 + 2 [/tex] A) Suppose h(x) is the result of g(x) undergoing a translation of 5 units to the right and 4 units up, and then a reflection over the y axis. find the coordinate of the vertex of h(x). B) A Transformation involving vertical and horizontal scale factors only [tex] h(x) \rightarrow ah(bx) [/tex] will bring the vertex of h(x) back to the vertex of g(x). Find the values of a and b (the rest of the function will *not* be the same as g(x)). 2. Relevant equations [tex] y = af[b(x-h)] + k [/tex] [/tex] 3. The attempt at a solution A) First i declared my translations: x -> x-5 y -> y -4 so far my function looks like this. y - 4 = (x-1-5)^2 + 2 y = (x-6)^2 + 6 now we have a reflection over the y axis. x -> -x, now my function looks like this. h(x) = (-x-6)^2 +6 So the vertex must be where h(x) = 6, so i sub y in for 6. and solve for x 6 = (-x-6)^2+6 and i get x = -6, so the vertex would be (-6, 6), graphing calculator confirmed this. B) this is where i encountered issues. a and b equal the same as h(x) because its just a reflection, in y = ah(b(x-h))+k i declared b = -1, and a = 1, is this the right way to show my answer? but just to show how i would get the vertex back to g(x)'s vertex, i also stated the values for h and k, h = -5, k = -4. and stated that g(x) = h(-x+5) - 4, is this correct?