Create a new function in the form y = a(x- h)^2 + k by performing the following transformations on f (x) = x^2

Chesley 2021-02-05 Answered

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.
h(x) is f (x) shifted right 3 units, stretched by a factor of 9, and shifted up by 7 units. \(h(x) = ?\)
Edit Coordinates of the vertex for the new parabola are:
\(x=?\)
\(y =?\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

likvau
Answered 2021-02-06 Author has 14318 answers

h(x) is f(x) shifted 3 units left. So, \(h(x)=f(x+3)\)
Then stretched by a factor of 2. So \(h(x)= 2f(x+3)\)
Reflected accross x axis. So, \(h(x) = -2f(x+3)\)
Then shifted up 7. \(h(x)= -2f(x+3)+7= -2(x+3)^2 + 7\)
Answer: \(h(x) = -2(x+3)^2 + 7\)
We compare h(x) with \(a(x-h)^2+k\). So \(h=-3\) and \(k=7\).
Vertex\(=(h,k)=(-3,7)\)
Answer:Vertex\(= (-3,7)\)
\(h(x)=-2(x+3)^2+7\)

Not exactly what you’re looking for?
Ask My Question
40
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-05

Given \(f(x)=x2\), after performing the following transformations: shift upward 58 units and shift 75 units to the right, the new function \(g(x)=\)

asked 2021-01-08

Graph by labeling three points and determine the type or types of transformations:
\(h(x)=\sqrt{x-2}-1\)

asked 2021-01-19

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
\(y=\sqrt{x - 2} - 1\)

asked 2020-12-12

Explain how you could graph each function by applying transformations.
(a) \(y = \log(x -2) + 7\)

(b) \(y = -3\log x\)

(c) \(y = \log(-3x)-5\)

asked 2020-11-23

Consider the scatterplot of y versus x in Output B.6 above.
a. Which power transformations on y should be considered to straighten the scatterplot?
b. Which power transformations on x should be considered to straighten the scatterplot?
image

asked 2020-11-30

Determine the matrix representation of each of the following composite transformations. A pitch of \(90^{\circ}\) followed by a yaw of \(90^{\circ}\)

asked 2021-02-11

Your friend attempted to describe the transformations applied to the graph of \(y=\sin x\) to give the equation \(f(x)=\frac{1}{2} \sin(-\frac{1}{3}(x+30))+1\).
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.

...