Question

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

Performing transformations
ANSWERED
asked 2021-02-05

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:
\(x=?\)
\(y =?\)

Answers (1)

2021-02-06

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\(= (-3,7)\)
\(h(x)=-2(x+3)^2+7\)

0
 
Best answer

expert advice

Need a better answer?

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 2021-01-19

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 2021-01-08

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

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 \(f(x)=1/2 \sin(-1/3(x+30))+1\).
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 2021-02-27

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
image

asked 2021-03-18

\(f(x)= \frac{-1}{3(x+1)}+1\)
Domain and range?
Transformations?
Name of Graph?

asked 2020-10-27

In this problem, allow \(T1: RR2 \rightarrow RR2 \text{ and } T2: RR2 \rightarrow R2\) be linear transformations. Find \(Ker(T_1), Ker(T_2), Ker(T_3)\) of the respective matrices
\(A=[(1,-1),(-2,0)],B=[(1,5),(-2,0)]\)

asked 2021-02-03

Lily wants to define a transformation (or series of transformations) using only rotations, reflections or translations that takes Figure A to Figure B.
image
Which statement about the transformation that Lily wants to define is true?
A. It can be defined with two reflections.
B.It can be defined with one rotation and one translation.
C. It cannot be defined because Figure A and Figure B are not congruent.
D.It cannot be defined because the longest side of Figure B is on the bottom.

...