Ask question

# 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 $$g(x) = −6(x−2)^2 + 5$$

### Relevant Questions

asked 2021-06-06
For each of the following functions f (x) and g(x), express g(x) in the form a: f (x + b) + c for some values a,b and c, and hence describe a sequence of horizontal and vertical transformations which map f(x) to g(x).
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2},{g{{\left({x}\right)}}}={2}+{8}{x}-{4}{x}^{{2}}$$
asked 2020-11-22
Functions f and g are graphed in the same rectangular coordinate system. If g is obtained from f through a sequence of transformations, find an equation for g.
(Graph given on the link)
asked 2020-11-08
Determine the transformations of the function f(x) to get the function $$g(x) =1/2f(5(x−3))−12$$ (The transformations happen in c, b, a, d order)
asked 2021-02-27
Functions f and g are graphed in the same rectangular coordinate system (see attached herewith). If g is obtained from f through a sequence of transformations, find an equation for g
asked 2020-11-27
Starting with the function $$f(x) = e^x$$, create a new function by performing the following transformations.
i. First shift the graph of f (x) to the left by two units.
$$f_1 (x) =$$?
ii. Then compress your result by a factor of $$1/7$$
$$f_2 (x) =$$ ?
iii. Next, reflect it across the x-axis.
$$f_3 (x) =$$ ?
iv. And finally shift it up by eight units to create g (x).
g (x) =?
asked 2021-01-15
Create a new function in the form $$y = a(x-h)^2 + k$$ by performing the following transformations on $$f (x) = x^2$$.
Give the coordinates of the vertex for the new parabola.
g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?
Coordinates of the vertex for the new parabola are:
x=?
y=?
asked 2021-02-11
Your friend attempted to describe the transformations applied to the graph of $$y=sinx$$ to give the equation $$f(x)=1/2sin(-1/3(x+30))+1$$.
They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.
asked 2021-01-23
Sketch the graph of the function $$f(x) = -2^x+1 +3$$ using transformations. Do not create a table of values and plot points
asked 2020-11-22
Given $$f(x)=x^2$$, after performing following transformations shift upwards 18 units and shift 89 units to the right, the new function g(x)=?
asked 2020-11-12
Given $$f(x)=x^2$$ after performing the following transformations shifted upwards 90 units and shifted 87 units to right, the new function g(x)=?
...