Following the order of operations, describe how the graph of y = x² has been transformed to create a new graph given the equation: y = -(1)/(2)(x + 4)² - 5

Question

Following the order of operations, describe how the graph of y = x² has been transformed to create a new graph given the equation: y =
`-(1)/(2)`(x + 4)² - 5

Answer 1

Explanation:

First we replace the original 'x' with 'x + 4,' which causes translation of the original parabolic graph 4 units to the left. Next, reflect this translated graph about the x-axis (which is the effect of multiplying by -1/2 as shown). Finally, shift the entire graph (the most recent one) down 5 units.