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
miss Akunina [59]
3 years ago
12

(b) Write a quadratic function, in standard form, that fits the set of points. Solve it as a system of three equations, and then

check your answers using the TI calculator. Refer to lesson 8.08 p. 314 in your textbook.
(-4, 9), (0, -7), and (1, -1)
Mathematics
1 answer:
Virty [35]3 years ago
4 0

Answer:

f(x) =2x^{2} +4x-7

Step-by-step explanation

Let equation be

f(x) =ax^{2} +bx+c

Since (-4,9) satisfy the  equation ,plugging x =-4 and f(x) = 9

f(x) =a(-4)^{2} +b(-4)+c

 9 = 16a -4b +c  ........ equation 1

plugging x =0 and f(x) = -7

-7 = a(0) +b(0) +c

gives c =-7 ......... equation 2

plugging x =1 and f(x) =-1

-1 = a(1) + b(1) +c

-1 = a+b+c ............. equation 3

From equation 2 ,we have c =-7

Plugging this value in equation in 1 and 3 ,we get

16a -4b -7 =  9

16a-4b= 9+7

16a-4b = 16

Dividing the equation by 4 ,we get

       4a -b = 4  ..........  equation 4

Plugging c =-7 in equation 1 ,we get

a+b+(-7) = -1

a+b = -1+7

a+b = 6 ......... equation5

Adding equation 4 and equation 5

 a+b =6

4a-b =4  

______________

5a = 10

a = 2

plugging a =2 in equation2

2+b = 6

 b = 6-2

 b = 4

therefore quadratic equation is

f(x) =2x^{2} +4x-7

             


You might be interested in
Solve for x and y.<br> 7x-4<br> #<br> 4y+8<br> 24#<br> +<br> 31
Darina [25.2K]

Answer:

7x-4 = -28

4y+8 = 4(y + 2)

Step-by-step explanation:

3 0
1 year ago
4 + 2x2(3x-5)<br> number of terms
igor_vitrenko [27]
3, assuming 2x2 is 2x squared, u will get
4 + 6x3 - 10x2

So 3 terms
7 0
3 years ago
The resistance of a wire varies directly with its length and inversely with the square of its diameter. If 100 feet of wire with
DaniilM [7]

Answer:

  14 ohms

Step-by-step explanation:

The resistance varies directly with length, so increasing the length by a factor will increase the resistance by the same factor.

__

The length of the wire increased by a factor of 1.4 from 100 ft to 140 ft. That means the resistance will increase by a factor of 1.4 from 10 ohms to 14 ohms. (The diameter did not change.)

The longer wire will have a resistance of 14 ohms.

4 0
2 years ago
Read 2 more answers
PLEASE HELP QUICK I AM IN A RUSH
Alekssandra [29.7K]
C because it simplifies to 0=0 which proves that it has infinite solutions!
7 0
3 years ago
Read 2 more answers
Kara did a survey to determine to study the types of pets that students in her school had. She surveyed 300 students and found t
julsineya [31]

Answer:

(C)81

Step-by-step explanation:

Total Number of Students =300

Percentage who had cats, n(C) = 40%

Percentage who had both cats and dogs , n(C \cap D) = 12%

Percentage who had neither cats nor dogs, n(C \cup D)' =45%

Now:

Universal Set, U = n(C)+n(D)-n(C \cap D)+n(C \cup D)'

100 = 40 + n(D)-12+45\\n(D)=100-73\\$Percentage of those who own dogs =27\%

Therefore:

Number of Students who had dogs

=27% of 300

=81

3 0
3 years ago
Other questions:
  • Which of these expressions is equivalent to log (12^8)
    11·2 answers
  • A ferry will safely accommodate 82 tons of passenger cars. Assume that the meanweight of a passenger car is 2 tons with standard
    15·1 answer
  • The set S consists of all odd multiples of 3: S = {..., -9, -3, 3, 9,...}. If the integers x and y are in S, then which of the f
    15·1 answer
  • Solve x2 - 4x = 12 by completing the square, show work please!!
    9·1 answer
  • A cube has a surface area of 9,600 square meters.<br> What is the volume of the cube?
    7·2 answers
  • Helphelphelphelphelphelphelphelphelphelphelp
    6·1 answer
  • A rectangular prism has a length of 9 inches, a height of 5 inches, and a width of 7
    13·1 answer
  • HELP ASAP PLZ Identify the angle relationships formed (spelling is important). Determine the value of x. Then determine the meas
    11·1 answer
  • Simplify the following cube root: cube root( 54x^6)
    14·2 answers
  • Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!