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

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Answer 1 · 2015-12-20T03:31:59

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

$y=(x$ $color(red)(+3))^2$
The graph shifts $3$ units to the left.
graph{(x+3)^2 [-10, 10, -5, 5]}

$y=color(red)(-)(x+3)^2$
The graph is reflected over the $x$ -axis.
graph{-(x+3)^2 [-10, 10, -5, 5]}

$y=-(x+3)^2$ $color(red)(-2)$
The graph is shifted $2$ units down.
graph{-(x+3)^2-2 [-10, 10, -7, 3]}

Describe the transformations applied to y=x²y=x² to obtain the graph of y=-(x+3)²-2y=-(x+3)²-2?