SOLUTION: What is the parent function and each individual transformation step for f(x)=-3x^2-5

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Question 1100203: What is the parent function and each individual transformation step for f(x)=-3x^2-5
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!
The parent function is f(x) = x^2:

graph%28400%2C400%2C-4%2C4%2C-50%2C20%2Cx%5E2%29

The graph is then reflected about the x-axis: f(x) = -x^2:

graph%28400%2C400%2C-4%2C4%2C-50%2C20%2C-x%5E2%29

Next the graph is stretched vertically by a factor of 3: f(x) = -3x^2

graph%28400%2C400%2C-4%2C4%2C-50%2C20%2C-3x%5E2%29

Note those first two transformations can be done in either order; or they can be combined into a single transformation "reflect in the x-axis and stretch vertically by a factor of 3"

Last the graph is translated down 5 units: f(x) = -3x^2-5:

graph%28400%2C400%2C-4%2C4%2C-50%2C20%2C-3x%5E2-5%29

It might be helpful to see the graphs of all the stages of the transformation on a single graph:

graph%28400%2C400%2C-4%2C4%2C-50%2C20%2Cx%5E2%2C-x%5E2%2C-3x%5E2%2C-3x%5E2-5%29

red: parent graph, f(x) = x^2
green: reflected about the x-axis, f(x) = -x^2
blue: stretched by a vertical factor of 3, f(x) = -3x^2
purple: translated down 5 units, f(x) = -3x^2-5