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
The price of a technology stock was $9.74 yesterday. Today, the price fell to $9.67. Find the percentage decrease. Round your an
agasfer [191]
% change = (new value - old value)/(old value) * 100%
.. = (9.67 -9.74)/9.74 * 100%
.. = -0.07/9.74 * 100%
.. = -0.7%

The decrease is 0.7%.
5 0
3 years ago
Let f(x)=x2−2x−4 . What is the average rate of change for the quadratic function from x=−1 to x = 4?
goblinko [34]

Answer:

The average rate of change for f(x) from x=−1 to x = 4 is, 1

Step-by-step explanation:

Average rate A(x) of change for a function f(x) over [a, b] is given by:

A(x) = \frac{f(b)-f(a)}{b-a}

As per the statement:

f(x) = x^2-2x-4

we have to find the average rate of change from x = -1 to x = 4

At x = -1

f(-1) = (-1)^2-2(-1)-4 = 1+2-4 = -1

and

at x = 4

f(4) = (4)^2-2(4)-4 = 16-8-4 = 4

Substitute these in [1] we have;

A(x) = \frac{f(4)-f(-1)}{4-(-1)}

⇒A(x) = \frac{4-(-1)}{4+1}

⇒A(x) = \frac{5}{5}

Simplify:

A(x) = 1

Therefore, the average rate of change for f(x) from x=−1 to x = 4 is, 1

4 0
3 years ago
Read 2 more answers
A slice is made parallel to the base of a right rectangular pyramid.
Bess [88]
Look like whatever <span>3.5×2</span> is. (7)
7 0
3 years ago
How much longer is dinner than the slide show?
shutvik [7]

Answer:

35

Step-by-step explanation:

7 0
2 years ago
What is 620,000 rounded to the nearest ten thousand
Sedaia [141]
620,000 rounded to the nearest thousand is:

620,000 because 2 is less than 5

Hope I Helped You!!!
5 0
3 years ago
Read 2 more answers
Other questions:
  • <img src="https://tex.z-dn.net/?f=%28x%20%2B%20k%29%20%7B%7D%5E%7B2%7D%20%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%201x%20%2B%20%20
    5·1 answer
  • If P(event A) = 0.25, what is P(not event A)?
    12·1 answer
  • A circle is translated according to the rule (x,y) → (x+10,-17). Which statement is true about the image of the circle after thi
    5·1 answer
  • PLEASE ANSWER !!! NEED DONE ASAP
    8·1 answer
  • What is 32,020.20 rounded to the nearest tenth?
    15·2 answers
  • Solve for x:<br> 9x + 10 = - 4x + 36<br> helppo pleasee !!!
    10·2 answers
  • ANSWER ASAP DUE AT 3:00 PM
    7·2 answers
  • Binomial Probability Distribution. How to determine the probability of one candidate of two winning.
    15·1 answer
  • Roberta is shopping at a bookstore. She starts with some money in her wallet, uses only cash
    12·1 answer
  • 5/7 - 3/2 in simplest form HELP ASAP
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!