SOLUTION: The function f(x) = x^2 is transformed to g(x)= - ½ (x+5)^2 + 4 What were the transformations that occured?

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Question 1170115: The function f(x) = x^2 is transformed to g(x)= - ½ (x+5)^2 + 4
What were the transformations that occured?
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


(1) The "-1/2" flips the graph vertically and shrinks it by a factor of 1/2.

(2) The "(x+5)" shifts the graph 5 units to the left.

(3) The "+4" shifts the graph up 4 units.

The order of the transformations is the order in which the expression would be evaluated for a given value of x:

parentheses first (shift 5 units left);
multiplication next (flip and shrink vertically);
addition last (shift 4 units up)

Here is a graph showing the incremental transformations:

red: original, x%5E2
green: translated 5 units left, %28x%2B5%29%5E2
blue: flipped and shrunken vertically, %28-1%2F2%29%28x%2B5%29%5E2
purple: translated 4 units up, %28-1%2F2%29%28x%2B5%29%5E2%2B4