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
vlabodo [156]
3 years ago
7

If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),

(4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!
Mathematics
2 answers:
Marrrta [24]3 years ago
8 0

Answer:

a = 3

b = 2

c = 0

d = -4

Step-by-step explanation:

Form 4 equations and solve simultaneously

28 = a(2)³ + b(2)² + c(2) + d

28 = 8a + 4b + 2c + d (1)

-5 = -a + b - c + d (2)

220 = 64a + 16b + 4c + d (3)

-20 = -8a + 4b - 2c + d (4)

(1) + (4)

28 = 8a + 4b + 2c + d

-20 = -8a + 4b - 2c + d

8 = 8b + 2d

d = 4 - 4b

Equation (2)

c = -a + b + d + 5

c = -a + b + 4 - 4b+ 5

c = -a - 3b + 9

28 = 8a + 4b + 2c + d (1)

28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b

28 = 6a - 6b + 22

6a - 6b = 6

a - b = 1

a = b + 1

220 = 64a + 16b + 4c + d (3)

220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b

220 = 60b + 100

60b = 120

b = 2

a = 2 + 1

a = 3

c = -3 - 3(2) + 9

c = 0

d = 4 - 4(2)

d = -4

lana66690 [7]3 years ago
7 0

Step-by-step explanation:

<u>Step 1:  Solve using the first point</u>

<em>(2, 28)</em>

28 = a(2)^3 + b(2)^2 + c(2) + d

28 = 8a + 4b + 2c + d

<u>Step 2:  Solve using the second point</u>

<em>(-1, -5)</em>

-5 = a(-1)^3 + b(-1)^2 + c(-1) + d

-5 = -a + b - c + d

<u>Step 3:  Solve using the third point</u>

<em>(4, 220)</em>

220 = a(4)^3 + b(4)^2 + c(4) + d

220 = 64a + 16b + 4c + d

<u>Step 4:  Solve using the fourth point</u>

<em>(-2, -20)</em>

-20 = a(-2)^3 + b(-2)^2 + c(-2) + d

-20 = -8a + 4b - 2c + d

<u>Step 5:  Combine the first and fourth equations</u>

<u />28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d

8 = 8b + 2d

8 - 8b = 8b - 8b + 2d

(8 -8b)/2 = 2d/2

4 - 4b = d

<u>Step 6:  Solve for c in the second equation</u>

-5 + 5 = -a + b - c + d + 5

0 + c = -a + b - c + c + d + 5

c = -a + b + d + 5

<u>Step 7:  Substitute d with the stuff we got in step 5</u>

c = -a + b + (4 - 4b) + 5

c = -a + b + 4 - 4b + 5

c = -a - 3b + 9

<u>Step 8:  Substitute d and c into the first equation</u>

<u />28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)

28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b

28 - 22 = 6a - 6b + 22 - 22

6 / 6 = (6a - 6b) / 6

1 + b = a - b + b

1 + b = a

<u>Step 9:  Substitute a, b, and c into the third equation</u>

220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)

220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b

220 - 100 = 60b + 100 - 100

120 / 60 = 60b / 60

2 = b

<u>Step 10:  Find a using b = 2</u>

a = b + 1

a = (2) + 1

a = 3

<u>Step 11:  Find c using a = 3 and b = 2</u>

c = -a - 3b + 9

c = -(3) - 3(2) + 9

c = -3 - 6 + 9

c = 0

<u>Step 12:  Find d using b = 2</u>

d = 4 - 4b

d = 4 - 4(2)

d = 4 - 8

d = -4

Answer:  a = 3, b = 2, c = 0,d = -4

You might be interested in
Which statement is true regarding the functions on the graph?
erastova [34]

Answer:

The answer to the questions Is f3=g6

8 0
3 years ago
How much money will you have at the end of one year if interest is compounded semiannually at 10% on a $600 deposit?
Masja [62]
The formula required to answer this is:
A=P(1+\frac{r}{n})^{nt}
where  A is the amount of the principal P after n compounding periods per year at r interest rate (as a decimal fraction).
Plugging in the given values, we get:
A=600(1+\frac{0.1}{2})^{2\times1}=661.5
Rounding to the nearest dollar, we get $662.00. Therefore a is the best answer choice.

6 0
3 years ago
I really need help with this question. Can I get a explanation too?
aniked [119]

Answer:

C

Step-by-step explanation:

Find the surface area:

Bottom base: 57 × 27 = 1,539

Top base: 21 × 27 = 567

Rectangular face: 23 × 27 = 621

Rectangular face: 23 × 27 = 621

Trapezoidal face: (21 + 57) ÷ 2 × 15 = 585

Trapezoidal face: (21 + 57) ÷ 2 × 15 = 585

1,539 + 567 + 621 + 621 + 585 + 585 = 4,518

The surface area is 4,518 square inches

3 0
3 years ago
If the probability of two events occurring together is 0, the events are called
Rainbow [258]

Answer:

disjoint

hope it helps plz mark me as brainliest

5 0
3 years ago
Joe was given $20 for his birthday.He then saved $10 per week from his allowance.Write a function to represent this situation
Inga [223]

Answer:

20 + 10w = total cash saved

7 0
3 years ago
Other questions:
  • Evaluate each expression for the given value 2/ 5 - 3 1 /2 for k = 15
    9·1 answer
  • Please give me the answer i have been working really hard sorry you have to help
    7·1 answer
  • Which formula defines the sequence f(1)=2, f(2)=6, f(3)= 10, f(4)= 14,f(5)=18
    13·1 answer
  • Need help with #21 please this is Algebra 2
    14·1 answer
  • A and B share the cost in a ratio of 3:2 the cost is £85 how much does A pay
    15·1 answer
  • Based only on the information given in the diagram, which congruence
    5·1 answer
  • Dominique deposited $3,000 into an account earning simple interest. The interest rate is 2.6%. How much interest will Dominique
    6·1 answer
  • F(x)=x+6 and g(x)=a-2 then find f(6)+g(4)
    7·1 answer
  • What is <br><img src="https://tex.z-dn.net/?f=f%284%29%20%3D%20%20%5Csqrt%7Bx%20%7B%7D%5E%7B2%7D%20%7D%20%20-%205" id="TexFormul
    8·1 answer
  • What is the least common multiple of 14 21 and 28​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!