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
FromTheMoon [43]
3 years ago
14

Find the quadratic function that passes through the points: (-1,6), (1,4), and (2,9).

Mathematics
1 answer:
Masja [62]3 years ago
8 0

Answer:

The quadratic function that passes through given points is                           y = 2 x² - x + 3  .

Step-by-step explanation:

The given quadratic function as

y = a x² + b x + c

The equation passes through the points ( - 1 , 6 ) , ( 1 , 4 ) and ( 2, 9 )

As The points passes through equation then

At points  ( - 1 , 6 )

6 = a (1)² + b ×( - 1 ) + c

Or, a - b + c = 6           .....A

Again At points  ( 1 , 4 )

4 = a (1)² + b × 1 + c

Or, a + b + c = 4            .......B

<u>Similarly At points  ( 2 , 9 )</u>

9 = a (2)² + b × 2 + c

Or, 4 a +2 b + c = 9        ....,,,C

<u>Now solving equation A and B</u>

(  a - b + c ) + (  a + b + c ) = 6 + 4

Or, a + c = \frac{10}{2}  

I.e a + c = 5           ......D

<u>Similarly Solving equation B and C</u>

( 4 a +2 b + c  ) - 2 × ( a + b + c ) = 9 - 2 × 4

Or, ( 4 a - 2 a + 2 b - 2 b + c - 2 c ) = 9 - 8

Or, ( 2 a - c ) = 1        .....E

<u>Solving D and E</u>

( a + c ) + ( 2 a - c ) = 5 + 1

Or, 3 a = 6

∴  a = \frac{6}{3}

I.e a = 2

<u>Put the value of a in Eq D</u>

So ,  a + c = 5

Or,  c = 5 - a

∴  c = 5 - 2 = 3

I.e  c = 3

<u>Put The value of a and c in Eq A</u>

a - b + c = 6      

Or, b = a + c - 6

Or . b = 2 + 3 - 6

∴ , b = 5 - 6

I.e   b = - 1

Now, <u>Putting the values of a , b , c in the given quadratic equation</u>

I.e y = a x² + b x + c

Or, y = 2 x² + ( - 1 ) x + 3

∴ The quadratic eq is  y = 2 x² - x + 3

Hence The quadratic function that passes through given points is                 y = 2 x² - x + 3  . Answer

You might be interested in
I need help on this geometry problem
crimeas [40]

Answer:

ST = 23

RU = 8

SV = 5

SU = 10


Step-by-step explanation:

UV = SV = 5

ST = UT = 23

RU = RS = 8

SU = SV + UV = 5 + 5 = 10


6 0
3 years ago
I am greater than 30 and less than 40. The sum of my digits is less than 5
Zielflug [23.3K]
The answer will be 31.
5 0
3 years ago
Read 2 more answers
Please help<br> me = lazy
forsale [732]

Answer:

1.)    13\frac{3}{10}\\

2.)11\frac{3}{4}\\

3.)11\\

4.)12\frac{1}{30}

5.)7\frac{11}{15}

6.) 5\frac{4}{5}

Step-by-step explanation:

I did 6 problems for you. You can now do the other 4 problems and see how I did it. You need to have the same denominator and the add the fractions together.

4 0
3 years ago
Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly s
GaryK [48]

Answer:

The bill size can be considered usual.

Step-by-step explanation:

Mean (μ) = $108.43

Standard deviation (σ) = $36.98

Now, consider the distribution to be normal distribution :

P(Z=\frac{X-\mu}{\sigma}>\frac{a-\mu}{\sigma})=P(Z>\frac{173-108.43}{36.98})\\\\\implies P(Z>1.75)

Now, finding values of z-score from the table. We get,

P(Z > 1.75) = 0.9599

⇒ 95.99%

So, only 4.01 % of the people in the city wastes water.

Hence, the bill size can be considered usual.

6 0
3 years ago
Read 2 more answers
Calculate the arithmetic sequence in which a9=17 and the common difference is d=-2.1
jek_recluse [69]

Answer:

S_{31}=71.3


Step-by-step explanation:

The nth term of an arithmetic sequence is given by the formula,

U_n=a_1+(n-1)d


We were given that the 9th term is 17.


\Rightarrow 17=a_1+(9-1)(-2.1)


\Rightarrow 17=a_1+(8)\times(-2.1)


\Rightarrow 17=a_1-\frac{84}{5}


\Rightarrow 17+\frac{84}{5}=a_1


\Rightarrow a_1=\frac{169}{5}


The sum of the first n-terms is given by the formula,


S_n=\frac{n}{2}(2a_1+(n-1)d)


To find S_{31}, we substitute n=31, a_1=\frac{169}{5} and d=-2.1.


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(31-1)(-2.1))


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(30)(-2.1))



\Rightarrow S_{31}=\frac{31}{2}(\frac{23}{5})


\Rightarrow S_{31}=\frac{713}{10}


\Rightarrow S_{31}=71.3


The correct answer is D















8 0
3 years ago
Read 2 more answers
Other questions:
  • Solve and graph (Look at pic.)
    15·1 answer
  • Help ASAP I will give a thanks and 5 stars
    15·1 answer
  • Ok so this is math question please help.
    11·1 answer
  • C is no the answer but can you help me???
    6·2 answers
  • Does anyone know how to do factoring? n^2-15n+56
    14·1 answer
  • Please help with this math question!
    11·1 answer
  • Help please the first person to get the answer will get the crown
    8·1 answer
  • What would x &amp; y be ? PLZ HELP DUE IN 20 MINUTES !
    9·1 answer
  • Pls help I’ll brainlest
    6·1 answer
  • Two exterior angles of a triangle measure 135° and 100°. What are the measures of the interior angles of the triangle?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!