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 \(g(x) = −6(x−2)^2 + 5\)

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 \(g(x) = −6(x−2)^2 + 5\)