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
RoseWind [281]
3 years ago
14

Given the following three points, find by hand the quadratic function they represent.

Mathematics
1 answer:
RideAnS [48]3 years ago
3 0

Answer:

The equation is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

The general form of a quadratic equation  or function f(x) is, f(x) = y = a·x² + b·x + c

Given that the points representing the quadratic function are;

(-1, -8), (0, -1), (1, 2) which  are of the form (x, y)

When x = -1, f(x) = y = -8

Plugging in the above values into the general form of a quadratic function, we have;

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8  = a - b + c.........................(1)

When x = 0, y = -1, we have;

-1 = a·(0)² + b·(0) + c = c

c = -1.......................................(2)

When x = 1, y = 2, which gives;

2 = a·(1)² + b·(1) + c = a + b + c

2 = a + b + c........................(3)

Adding equation (1) to equation (3), we have;

-8 + 2 = a - b + c + a + b + c

-8 + 2 = 2·a + 2·c

From equation (2) c = -1, we get;

-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)

-6 = 2·a - 2

-4 = 2·a

a = -2

From equation (3), we have

2 = a + b + c

Substituting the values of a, and c gives;

2 = -2 + b - 1

b = 2 + 2 + 1 = 5

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1.

You might be interested in
PLEASE HELP ME!! I WILL GIVE YOU BRAINLIEST AND 50 POINTS!! AND DON'T JUST PUT YES, NO AND THEN NUMBERS, *USE COMPLETE SENTENCES
viva [34]

Answer:

John Muir

John Muir was an American naturalist born in Scotland on April 21, 1838. Step-by-step explanation:

8 0
2 years ago
ashton is saving money to buy a new bike. he needs $120 but has only saved 60% so far. How much more money does Ashton need to b
Tasya [4]
Ashton has saved: 60% of $120=(60/100)*$120=(60*$120)/100=$72
Ashton need to buy the bike=$120-$72=$48

He needs to buy the bike=$48
5 0
3 years ago
A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?
Zina [86]

The correct answer is p/rs.

In order to find this first state the direct variation with the constant k included.

p = krs

Now to find the value of k, we simply divide away the r and s

p/rs = k

3 0
2 years ago
Read 2 more answers
Which number is a solution to the inequality? m > 2/3
andrew11 [14]
C. 1
It's because 2/3 is equal to 0.6666667
1 is the only greater than that since they're all negative options
4 0
3 years ago
Please help, photo attached.
steposvetlana [31]

The zeroes of the polynomial functions are as follows:

  • For the polynomial, f(x) = 2x(x - 3)(2 - x), the zeroes are 3, 2
  • For the polynomial, f(x) = 2(x - 3)²(x + 3)(x + 1), the zeroes are 3, - 3, and -1
  • For the polynomial, f(x) = x³(x + 2)(x - 1), the zeroes are -2, and 1

<h3>What are the zeroes of a polynomial?</h3>

The zeroes of a polynomial are the vales of the variable which makes the value of the polynomial to be zero.

The polynomials are given as follows:

f(x) = 2x(x - 3)(2 - x)

f(x) = 2(x - 3)²(x + 3)(x + 1)

f(x) = x³(x + 2)(x - 1)

For the polynomial, f(x) = 2x(x - 3)(2 - x), the zeroes are 3, 2

For the polynomial, f(x) = 2(x - 3)²(x + 3)(x + 1), the zeroes are 3, - 3, and -1

For the polynomial, f(x) = x³(x + 2)(x - 1), the zeroes are -2, and 1

In conclusion, the zeroes of a polynomial will make the value of the polynomial function to be zero.

Learn more about polynomials at: brainly.com/question/2833285

#SPJ1

5 0
1 year ago
Other questions:
  • if a set covers a range of points, including those between isolated points, and cannot be written as a list, it is called
    11·1 answer
  • At a track meet, Tim ran at a constant speed of 300 meters per minute. After 8 minutes, he still had 600 meters left to run. The
    11·1 answer
  • Use the segment to complete the statements.
    5·1 answer
  • 14 =root 121√√...........​
    13·1 answer
  • Please help me with 1-5
    6·2 answers
  • Math help is needed ps how is your day going ?
    5·2 answers
  • The volume of a swimming pool is 4x^3 - 20x^2 + 3x - 15 . what is one of the dimensions of the pool
    15·1 answer
  • Write and Solve an equation to determine the missing dimension of the prism with a volume of 160cm. Height is missing the number
    8·1 answer
  • The angles shown below are supplementary:
    8·1 answer
  • A prism with a heart-shaped base is sliced parallel to the base. What shape is formed?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!