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
Stella [2.4K]
3 years ago
5

Find a second-degree polynomial (that is, an equation of the form y =a + bx + cx2 d that goes through the three points (0, 1), (

1, 0), and (-1, 0). Is there more than one possibility?

Mathematics
1 answer:
Lostsunrise [7]3 years ago
8 0

Answer:

y = 1 - x^2

Step-by-step explanation:

we're given three points (0,1),(1,0) and (-1,0). and and equation of a parabola

y = a + bx + cx^2

we can plug in each of the coordinates, and 3 equations

(x,y) = (0,1)

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

a=1\quad\quad\Rightarrow A

(x,y) = (1,0)

0 = a + b(1) + c(1)^2

a + b + c=0\quad\quad\Rightarrow B

(x,y) = (-1,0)

0 = a + b(-1) + c(-1)^2

a - b + c=0\quad\quad\Rightarrow C

These are are three equations, well we can simultaneously solve them to find the values of a, b and c.

we already found that, a = 1. so we plug this value in the rest of the equations. we'll use equation B.

a + b + c=0

1 + b + c=0

b=-1-c

we can substitute this value of b and a = 1, equation C

a - b + c=0

1 -(-1-c) + c=0

1 +1+c + c=0

2+2c=0

c=-1

we can use this value of c back in b

b=-1-(-1)

b=0

hence our equation of the 2-degree polynomial will be:

y = a + bx + cx^2

y = 1 + (0)x + (-1)x^2

y = 1 - x^2

and this polynomial indeed passes through all the points (0, 1), (1, 0), and (-1, 0).

And since these are the only solutions to the simultaneous equation we solved (i.e. we have single values of a,b and c). there's no other possibility.

You might be interested in
HELP THIS IS SO IMPORTANT
LekaFEV [45]

Answer:

variable = s

sum = 10

product = 20

i dont know the last one

brainlest please

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What is the length of the apothem of a regular hexagon with 10-cm sides?
vodka [1.7K]

Answer:

The length of apothem of given hexagon is 8.66 cm

Step-by-step explanation:

Apothem of a polygon is given by:

apothem = \frac{s}{2\ tan\ (\frac{180}{n})}

Here

s is length of side

tan is trigonometric function

and n denotes number of sides

Given that the polygon is a hexagon

s = 10cm\\n = 6

Putting the values in the formula

apothem = \frac{10}{2\ tan\ (\frac{180}{6})}\\= \frac{10}{2\ tan\ 30}\\=\frac{10}{2 * 0.5773}\\=\frac{10}{1.1546}\\=8.6610\\Rounding\ off\ to\ nearest\ hundredth\\= 8.66\ cm

Hence,

The length of apothem of given hexagon is 8.66 cm

6 0
3 years ago
The following table shows a proportional relationship between x and y.
RUDIKE [14]

Answer:

Assume x is directly proportional to y :

y \:  \alpha  \: x \\ y = kx

when y is 9, x is 2:

substitute to find value of k :

9 = (k \times 2) \\ k =  \frac{9}{2}

Therefore, equation is:

{ \boxed{ \boxed{2y = 9 x}}}

8 0
2 years ago
What is the definition of supplementary angles.
never [62]

Answer: either of two angles whose sum is 180°.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
2. (-4) - 3- 1- 8<br><br> A) -10 <br><br> B)-16<br><br> C) -19 <br><br> D) -8
DedPeter [7]

Answer:

B) -16

Step-by-step explanation:

-4-3-1-8

subtract them all lol

7+9= 16

Then add the negative symbol

-16

7 0
3 years ago
Read 2 more answers
Other questions:
  • (2x + 3) (x² + x - 2)
    14·2 answers
  • HELP PLEASE???<br> ?????<br> ????<br> ???
    10·1 answer
  • What is the answer too -4(3a-5b-7)
    11·1 answer
  • Write the value of the 6 in 106,534
    11·2 answers
  • Jim has 6 quarters, 1 dime, 5 nickels, and 2 pennies in his pocket. If one coin falls from his pocket, what is the probability t
    8·1 answer
  • What is the range of the function on the graph?
    12·2 answers
  • Help ASAP!!! Problem is on the picture provided.
    14·2 answers
  • 4. John wants to cover a box entirely with silver paper. How many square centimetres
    13·1 answer
  • Guys thank you for everyone who has helped me im almost done​
    8·1 answer
  • 1. How many minutes until quarter of TEN?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!