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.

Question
Performing transformations
asked 2021-02-23
List a sequence of transformations, in words, to convert the graph of \(f(x)=x^2\) into the graph of \(g(x)=-6(x-2)^2+5\).

Answers (1)

2021-02-24
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 \(g(x) = −6(x−2)^2 + 5\)
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