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
Readme [11.4K]
4 years ago
11

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Mathematics
1 answer:
Lisa [10]4 years ago
6 0

Answer:

f(x) = 4x^2 - 3x + 6

Step-by-step explanation:

Quadratic function is given as f(x) = ax^2 + bx + c

Let's find a, b and c:

Substituting (0, 6):

6 = a(0)^2 + b(0) + c

6 = 0 + 0 + c

c = 6

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

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

16 = a(2)^2 + b(2) + 6

16 = 4a + 2b + 6

16 - 6 = 4a + 2b + 6 - 6

10 = 4a + 2b

10 = 2(2a + b)

\frac{10}{2} = \frac{2(2a + b)}{2}

5 = 2a + b

2a + b = 5 => (Equation 1)

Substituting (3, 33), and c = 6

f(x) = ax^2 + bx + x

33 = a(3)^2 + b(3) + 6

33 = 9a + 3b + 6

33 - 6 = 9a + 3b + 6 - 6

27 = 9a + 3b

27 = 3(3a + b)

\frac{27}{3} = \frac{3(3a + b)}{3}

9 = 3a + b

3a + b = 9 => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

3a + b = 9

2a + b = 5

a = 4

Replace a with 4 in equation 2.

2a + b = 5

2(4) + b = 5

8 + b = 5

8 + b - 8 = 5 - 8

b = -3

The quadratic function that represents the given 3 points would be as follows:

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

f(x) = (4)x^2 + (-3)x + 6

f(x) = 4x^2 - 3x + 6

You might be interested in
How can I solve 2 3/4 - {1/2 + (1/3)}
Diano4ka-milaya [45]
Do what’s in the brackets first it should be 23/12 or 1 11/12 or 1.916
6 0
3 years ago
A doctor studying nutrition collected data on the heights (in meters) in children in America.
Alexus [3.1K]

Answer:

I need to know the full question. will you be my friend

Step-by-step explanation:

plz

5 0
4 years ago
What is the slope intercept form of (2,6), (-4,-6)
victus00 [196]
Find slope first using slope formula.
m= (y2-y1)/(x2-X1)
m= 3/2

So the slope intercept form is

y-6= 3/2 (x-2)


5 0
3 years ago
Find the area of the circle. Leave your answer in terms of pi.
Tom [10]
<h2>Answer:</h2>

A=4.2025\pi

<h2>Step-by-step explanation:</h2>

A circle is a curve made up of all the points having the same distance from the center. In terms of the diameter, that is any chord that passes through the center, the area can be found as:

A=\pi (\frac{d}{2})^2

We know that d=4.1m then:

A=\pi (\frac{4.1}{2})^2 \\ \\ A=\pi (2.05)^2 \\ \\ A=4.2025\pi

So 4.2025\pi is the result and as you can realize this area is in terms of π

7 0
3 years ago
To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with 8 cups of water. Pa
n200080 [17]

Answer:

The tables are given below and

since,

 \frac{4}{6} = \frac{16}{24} > \frac{15}{24} = \frac{5}{8}

so, Noah's mixture will taste more like orange, than Andre's mixture.              

 

Step-by-step explanation:

To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water, Andre mixes 5 scoops of powder with 8 cups of water.

so, can construct the following tables -

A) table that shows  different amounts of powder and water that taste the same as Noah's mixture :-

Serial no.  Powder in  scoops       cups of water

      1                 8                                   12

      2               12                                   18

      3               16                                    24

      4.               20                                   30

      5.               24                                   36              

B) table that shows  different amounts of powder and water that taste the same as Andre 's mixture :-

Serial no.  Powder in  scoops       cups of water

      1                 10                                   16

      2                15                                   24

      3                20                                   32

      4.               25                                   40

      5.               30                                   48

C) Since,

 \frac{4}{6} = \frac{16}{24} > \frac{15}{24} = \frac{5}{8}

so, Noah's mixture wili taste more like orange, than Andre's mixture.              

6 0
3 years ago
Other questions:
  • Alexa drew a scale drawing of a swimming pool. The pool is 3 centimeters wide in the drawing. The actual pool is 18 meters wide.
    13·1 answer
  • Abandoned mines frequently fill with water. Before an abandoned mine can be reopened, the water must be pumped out. The size of
    14·1 answer
  • Solve for m
    9·1 answer
  • Given a right cylinder where h is the height and ris the radius, what does the
    8·1 answer
  • How do u find original price if the sales tax is 9%
    9·1 answer
  • What is the image point of (1,4) after a translation left 5 units and down 5 units
    11·1 answer
  • Which fractions add together to make 3/6
    15·1 answer
  • How do i work out -2=6+a/5
    6·2 answers
  • after buying one bottle caps for 27.70 richard has 19.15 left how much money did richard have to begin with???
    14·1 answer
  • A jellyfish travels 3/5 mile in 1/6 hour and a walrus travels 5/6 mile in 3/10 hour. Which animal is faster?​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!