Question

How do you describe the transformation of `f(x)=2-(x+5)^2` from a common function that occurs and sketch the graph?

Answer 1

This way.

Explanation:

Consider y= `x^2` as the starting common function.

Now , `x^2`------>`(x+5)^2` involves a leftward (negative) direction shift of 5 units.

Then, `(x+5)^2`------> `- (x+5)^2` means we have to take a mirror image about the x axis.

Then, `- (x+5)^2` ------> `2- (x+5)^2` involves shift along y axis in the positive or upper direction .

Hence, we get the required graph.

graph{2- (x+5)^2 [-10, 10, -5, 5]}