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
Montano1993 [528]
3 years ago
14

Given that f(x) =3x^2 - 6x + 11 ,find the values of a,b and c for which f(x) = a(x - b)^2 + c

Mathematics
1 answer:
V125BC [204]3 years ago
3 0
First you have to complete the square. The first step would be 3x^2-6x=-11. Then you divide -6 by 2 and square the number you get. 3x^2-6x+9=-11+9. 3x^2-6x+9=-2. Factor out the three to get 3(x^2-2x+3)=-2. You can't factor what is in the parenthesis. You should then add two to each side. 3(x^2-2x+3)+2.A = 3B= I don't knowC = 2
You might be interested in
HELPPPP!!!
Hatshy [7]

Answer:

(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1 where a > b

- So lets collect x in a bracket and make it a completing square and

  also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x + 16y - 31 = 0

∴ (x² - 2x) + (-4y² + 16y) - 31 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y² - 4y) - 31 = 0

∴ (x² - 2x) - 4(y² - 4y) - 31 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵  (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

   the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1

- We will do the same withe bracket of y

- Lets make 4(y² - 4y) completing square

∵ √y² = y

∴ The 1st term in the bracket is x

∵ 4y ÷ 2 = 2y

∴ The product of the 1st term and the 2nd term is 2y

∵ The 1st term is y

∴ the second term = 2y ÷ y = 2

∴ The bracket is 4(y - 2)²

∵ 4(y - 2)² = 4(y² - 4y + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out

   the bracket to keep the equation as it

∴ 4[y² - 4y + 4) - 4]

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify

∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms

∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides

∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - (y - 2)²/4 = 1

∵ 16 = (4)² and 4 = (2)²

∴ The standard form of the equation of the hyperbola is

   (x - 1)²/4² - (y - 2)²/2² = 1

4 0
3 years ago
Water starts out at a temperature of 62 F . It is heated such that its temperature increases at a rate of 8 F per minute. It tak
bogdanovich [222]

Answer:

Step-by-step explanation:

since it starts at 62 and finishes at 150 u can find out that the increase in temp is 150F and since it increases by 8 every minute u can come to find that the increase in temp (150) divided by the amount it increases 8 is 18.75 which is the amount of minutes it took

7 0
2 years ago
Read 2 more answers
Which of the following data sets contain an outlier?
AURORKA [14]

Answer:

Step-by-step explanation:

7 0
3 years ago
Solve this equation: -88=5y-13
nadya68 [22]

Answer:

y=-15

Step-by-step explanation:

4 0
3 years ago
What is the solution to the inequality? 17 < 9 + x
dezoksy [38]

Answer:

x > 8

Step-by-step explanation:

Given

17 < 9 + x ( subtract 9 from both sides )

8 < x , hence

x > 8

7 0
3 years ago
Other questions:
  • HELPPP PLEASE <br>50 POINTSS​
    10·1 answer
  • Which represents an exterior angle of triangle ABF?<br><br>∠BAD<br>∠AFE<br>∠CAD<br>∠CAB​
    9·2 answers
  • Simplify the expression (64)2
    15·2 answers
  • zoe paid $18.60 in sales tax and tips for her dinner. The sales tax rate is 11%, and she tipped 20%. (the sales tax does not app
    10·1 answer
  • Can you help me please for number 8
    13·1 answer
  • D/3 = 19 <br><br> what is d?<br><br> d = ?
    15·2 answers
  • What matches with Pictograph??
    8·2 answers
  • Work out the angle x please help.
    8·2 answers
  • Help is needed DESPERATLY
    8·2 answers
  • What is 81 to the 1/4 power
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!