1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Orlov [11]
3 years ago
15

If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

unction g(x) in vertex form.
a. f(x) = 1/2(x - 11)^2 - 5
b. f(x) = 1/2(x + 11)^2 - 5
c. f(x) = 2(x - 11)^2 - 5
d. f(x) = 2(x + 11)^2 - 5

If the parent function f(x) = x^2 is fatter translated 8 units to the right, then translated 1 unit down, write the resulting function g(x) in vertex form.
a. g(x) = 1/3(x - 8)^2 - 1
b. g(x) = 1/3(x + 8)^2 - 1
c. g(x) = 3(x - 8)^2 - 1
d. g(x) = 3(x + 8)^2 - 1
Mathematics
1 answer:
nikklg [1K]3 years ago
7 0

The quadratic function given by:


f(x)=a(x-h)^2+k, \ \ \ a\neq 0


is in vertex form. The graph of f is a parabola whose axis is the vertical line x=h and whose vertex is the point (h, k). So:


To translate the graph of a function to the right, left, upward or downward we have:

For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)


By knowing this things, we can solve our problem as follows:


FIRST.

  • Translating <em>11 units to the left:</em>

g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2


  • Then translating<em> 5 units down:</em>

g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5


Since the new function is fatter, the factor we need to multiply the term (x+11)^2 <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.


<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>


SECOND.

  • Translating <em>8 units to the right:</em>

g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2


  • Then translating<em> 1 unit down:</em>

g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1


As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.


<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

You might be interested in
What's the answer????
Svetllana [295]
I would try b the rise\run is 2\2 so give it a go
8 0
3 years ago
SHOW STEP BY STEP FOR BRAINLIEST
Nostrana [21]

Answer:

The y-coordinate of F is 8.

Step-by-step explanation:

The area of the large triangle = 1/2 * base * height.

From the given coordinates:

The base of the large triangle =  x coordinate of C - x coordinate of A

= 11 - 3 = 8 units.

It's height = y coordinate of A = 12, so

Area of large triangle = 1/2 * 8 * 12 = 48 unit^2.

Using a similar calculation for the small triangle:

Base = 10 - 6 = 4 and height = k units.

So it's area = 1/2 * 4 * k = 2k unit^2.

So from given area of the shaded part:

48 - 2k = 32

-2k = -16

k = 8.

8 0
3 years ago
Can someone help me with these questions? i’m so lost
spayn [35]

Answer:

Q.5 ab=cd

Q.6 ad=bc

Q.7 ce=ae

Q.8 eb=ed

Q.9 angle D=angle B (opposite angle of parallelogram are equal)

let other angle of parallelogram be x.

angle A+angle B +angle C + angle D= 360° (sum of quadrilateral is 360°)

x+130°+x+130°=360°

2x+260°=360°

2x=360°-260°

2x=100°

x=100/2

x=50°

Q.10 similarly, angle b= angle d

let other angle be x.

x+61°+ x+61°=360°

2x+122°=360°

2x=360°+122°

2x=238°

x=238°/2

x=119°

Q.11 in quadrilateral opposite angles are equal and opposite angle of parallelogram are equal.

Q.12 in quadrilateral opposite angle are equal and opposite angle of parallelogram are equal.

Q.13 in quadrilateral opposite sides are equal and opposite sides are parellel and this property is also present in parallelogram.

q.14 in quadrilateral diagonal bisected each other and diagonal of parallelogram also bisect each other.

8 0
3 years ago
Which number is the greatest? 0.35, 0.2, 0.56, 0.8, 0.09
ludmilkaskok [199]
I do believe it is 56
8 0
3 years ago
Read 2 more answers
Determine if the expression - x^3 y^5 / 3 is a polynomial or not. If it is a polynomial, state the type and degree of the polyno
kykrilka [37]

Answer:

it is not a polynomial it has no degree either .. and we only classify polynomials in accordance with their degrees

4 0
2 years ago
Other questions:
  • What interger is equivalent to 25 3/2
    12·2 answers
  • The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover the block entirely wit
    13·1 answer
  • Graph the data. then find and interpret the slope of the line through the points.
    13·1 answer
  • 6. Hank can type 24 words per minute. Hank starts
    12·1 answer
  • Solve for s 2* s= 1.2 what is it​
    12·2 answers
  • A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 c
    7·1 answer
  • A jar contains 3 blue marbles and 6 red marbles. Suppose you choose a marble at
    14·1 answer
  • Guess a number from 1-10 for 100 points!
    11·1 answer
  • If BCDE is congruent to OPQR then DE is congruent to what?
    12·1 answer
  • You go outside and step on a frog, the sand is yellow because the grass was 42, therefore the rabbit hopped 39 degrees upwards.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!