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
goldenfox [79]
3 years ago
8

The graph shows g(x), which is a translation of f(x) = x^2. Write the function rule for g(x). Show step by step.

Mathematics
1 answer:
Mariana [72]3 years ago
3 0

Answer:

g(x)=(x-7)^2+6

g(x) is a translation of f(x) 7 units to the right and 6 units up.

Step-by-step explanation:

Let the equation of the function g(x) be

g(x)=a(x-b)^2+c

This curve passes through the points (9,10), (5,10) and (7,6), then their coordinates satisfy the equation:

10=a(9-b)^2+c\\ \\10=a(5-b)^2+c\\ \\6=a(7-b)^2+c

Subtract the second equation from the first:

10-10=a(9-b)^2+c-a(5-b)^2-c\\ \\0=a((9-b)^2-(5-b)^2)\\ \\a\neq 0\ \text{then}\ (9-b)^2-(5-b)^2=0\\ \\(9-b)^2=(5-b)^2\\ \\9-b=5-b\ \text{or}\ 9-b=b-5\\ \\9=5\ \text{false}\\ \\2b=14\\ \\b=7

Then

10=a(9-7)^2+c\\  \\6=a(7-7)^2+c

So,

10=4a+c\\  \\6=c

Hence,

c=6\\ \\b=7\\ \\10=4a+6\Rightarrow a=1

The expression for g(x) is

g(x)=(x-7)^2+6

g(x) is a translation of f(x) 7 units to the right and 6 units up.

You might be interested in
Volume of the cylinder with diameter of 8mm and height of 8mm
alexdok [17]

Answer:

V = 402.12385mm

Step-by-step explanation:

When the diameter is 8mm, the radius is 4mm.

V = (π(4^2))8

V = (16π)8

V = (50.2654)8

V = 402.12385

V ≈ 402, 402.1, 402.12, 402.124

4 0
2 years ago
ANSWER FOR BRAINLYEST THANK U!
Juli2301 [7.4K]
B.

-62 + 50 = -12

He is 12 dollars above the $50 limit, account will be closed.
5 0
2 years ago
(¡¡Please help!!)
Gnoma [55]

Answer:

Step-by-step explanation:

D is the answer

7 0
2 years ago
Read 2 more answers
Please i need help ! its due today ! Class A has 10 pupils and class B has 17 pupils.
Rudiy27

Answer:

The mean score is 87

Step-by-step explanation:

79x2=158

158-71=87

6 0
1 year ago
On Dec. 4, 1998, sunrise was at 6:58 and sunset was at 4:12.
zhuklara [117]
The length of the daylight was 9 hr 10 min
6 0
2 years ago
Other questions:
  • Domain of the function
    12·1 answer
  • Larry stencils this pattern to make a border at the top of his bedroom walls. Describe the pattern. Draw what might be the missi
    6·2 answers
  • 45-7=35 is an addend or equation
    12·2 answers
  • A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the tr
    14·1 answer
  • What is the next number: 747, 757, 766, 774, 781,787, 792, ... *
    8·2 answers
  • A cereal box's length is 25 cm, height is 30 cm and width is 10 cm.
    6·1 answer
  • Toni is tossing 2 coins. What is the probability of landing a heads and then landing another heads?
    11·2 answers
  • Please help me out!!!!!
    15·1 answer
  • In 2019, Company A purchased a commercial building with 8 retail units for $4,200,000. In 2021, Company A decided to sell this b
    6·1 answer
  • this is about similar triangles :)which of the following statements is true about similar triangles?the measurements of correspo
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!