# List a sequence of transformations, in words, to convert the graph of f(x)=x^2 into the graph of g(x)=-6(x-2)^2+5.

List a sequence of transformations, in words, to convert the graph of $$f(x)=x^2$$ into the graph of $$g(x)=-6(x-2)^2+5$$.

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Macsen Nixon
Given
We have to convert the graph of $$f(x) =x^2$$ into the graph of $$g(x) = −6(x−2)^2 + 5$$
Now, listing a sequence of transformations
we have $$f(x) =x^2$$
Multiplying $$x^2$$ by -6 we get, $$−6x^2$$. It will flip the graph and vertically stretch the graph, so that the ratio of the ordinate of points will be 6 :1 .
Now converting $$−6x^2 to −6(x−2)^2$$. It will shift the graph horizontally right.
Now converting $$−6(x−2)^2 to −6(x−2)^2 + 5$$. It will shift the graph vertically upward .
now we will get the graph of $$g(x) = −6(x−2)^2 + 5$$