Question

Describe the transformations applied to  y=x²  to obtain the graph of              y=-(x+3)²−2 ?

Answer 1

y=x²

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

 

y=(x +3)²

The graph shifts 3 units to the left.

graph{(x+3)^2 [-10, 10, -5, 5]}

 

y=−(x+3)²

The graph is reflected over the x-axis.

graph{-(x+3)^2 [-10, 10, -5, 5]}

 

y=−(x+3)²−2

The graph is shifted 2 units down.

graph{-(x+3)^2-2

[-10, 10, -7, 3]}

which is above transformation to the given graphs.