find an equation in standard form of the parabola passing through the points (0, - 1), (1, 5), (- 1, - 5)

Answers

Answer 1

Answer:

The equation of the parabola in standard is [tex]y=x^{2}+5x-1[/tex]

Step-by-step explanation:

The standard form equation of the parabola is:

[tex]y=ax^{2}+bx+c[/tex]

Using the three points we can find a, b and c.

Let's put the first point (0,-1)into the standard form equation.

[tex]-1=a(0)^{2}+b(0)+c[/tex]

[tex]c=-1[/tex]

Using the second point (1,5) and the value of c found above.

[tex]5=a(1)^{2}+b(1)+c[/tex]

[tex]5=a+b-1[/tex]

[tex]6=a+b[/tex] (1)

Finally using the las point (-1,-5)  

[tex]-5=a(-1)^{2}+b(-1)+c[/tex]

[tex]-5=a-b-1[/tex]

[tex]-4=a-b[/tex] (2)  

Solving the system of equations (1) and (2) we can find a and b.

[tex]6=a+b[/tex]

[tex]-4=a-b[/tex]

Adding both of them we have:

[tex]2=2a[/tex]

[tex]a=1[/tex]

And b = 5.

Therefore, the equation of the parabola in standard form will be.

[tex]y=x^{2}+5x-1[/tex]

I hope it helps you!  


Related Questions

The two-way table shows the number of books of each type in Eliza’s home.

A 5-column table has 3 rows. The first column has entries hardcover, paperback, total. The second column is labeled Fiction with entries 28, 4, 32. The third column is labeled biographies with entries 2, 1, 3. The fourth column is labeled Reference with entries 10, 15, 25. The fifth column is labeled Total with entries 40, 20, 60.

What is the probability that a randomly selected reference book is hardcover?

0.25
0.4
0.6
0.75

Answers

The answer is 0.4 hope it helps!

The probability that a randomly selected reference book is hardcover is 0.4.

The two-way table depicts the distribution of books in Eliza's home by type (hardcover, paperback, biographies, fiction, and reference), as well as the number of books in each category (32 fiction books, 3 biographies, and 25 reference books).

There are a total of 25 reference books, of which 10 are hardcover.

So the probability that a randomly selected reference book is hardcover is:

10/25 = 0.4

Therefore, the probability is: 0.4.

For more details regarding probability, visit:

https://brainly.com/question/30034780

#SPJ7

A biology student wants to determine if using a fertilizer would help promote the growth of new babies in spider plants. The student has access to 90 baby spider plants of three varieties: green, variegated, and curly. There are 30 plants of each variety. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. The numbers 1–30 are written on slips of paper, placed in a hat, and mixed thoroughly. A plant is selected and a slip of paper is drawn. If the slip has the numbers 1–15, then the plant will receive fertilizer. If the slip has the numbers 16–30, the plant will not receive fertilizer. A green spider plant is selected and a slip of paper is drawn. This plant is placed in the treatment group indicated by the number, and the slip is not put back in the bag. The slips are mixed again, the next green spider plant is selected, and a slip is drawn. The plant is placed in the treatment group indicated by the number. This procedure is repeated until all 30 green spider plants are assigned to treatments. The numbered slips are placed back in the bag and this procedure is repeated for the remaining types of spider plants. After one year, the shoots will be counted for each plant.

Which of the following best describes the design for this experiment?

observational study
matched pairs design
randomized block design
completely randomized design

Answers

Answer:

Randomized block design

Step-by-step explanation:

From the question, we can see the following:

- There are 30 plants of each variety. This means that they are divided into variety subgroups which we will call blocks.

- Now, we are told each plant in each block all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. This means that each plant in each block is assigned a treatment condition.

- The procedure is repeated by subjecting each plant one after the other in teach Block to different treatments and this will reduce variability.

Looking at all the statements above, it is clear that this is a randomized block design because a randomized block design is when the experimenter/researcher divides members/participants into subgroups called blocks in a manner that the variability within the blocks is less than the variability between the blocks. Thereafter, the participants within each block will now be randomly assigned to treatment conditions.

The best describe about the design for this experiment is random block design.

A randomized block design is an experimental design where the experimental units are in groups called blocks. The treatments are randomly allocated to the experimental units inside each block.

When all treatments appear at least once in each block, we have a completely randomized block design.

There are 30 plants of each variety. This means that they are divided into variety subgroups which we will call blocks.

Each plant in each block all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light.

This means that each plant in each block is assigned a treatment condition.

The procedure is repeated by subjecting each plant one after the other in teach Block to different treatments and this will reduce variability.

The statements above, it is clear that this is a randomized block design because a randomized block design is when the experimenter/researcher divides members/participants into subgroups called blocks.

In a manner that the variability within the blocks is less than the variability between the blocks. Thereafter, the participants within each block will now be randomly assigned to treatment conditions.

Hence, The best describe about the design for this experiment is random block design.

To know more about Random block design click the link given below.

https://brainly.com/question/20165310

Which graph represents the function y=-(x-2)²+3?

Answers

Answer:

Graph D

Step-by-step explanation:

the bottom right graph represents the function  y=-(x-2)²+3. I put it in a graphing calculator soo

If Arron's boat travels 9 mph and the river runs 4 miles mph in still water.how long will it take to travel 18 miles upstream

Answers

Answer:  It will take Aaron's boat 3³/₅ hours to travel 18 miles upstream.

That is 3.6 hours or  3 hours and 36 minutes.

Step-by-step explanation:

Traveling upstream, the boat's speed will be reduced by the speed of the river current.  

9 - 4 = 5mph

18mi/5mph =  3.6 hours  0r  3³/₅ hours

40% of x is 35 Write an equation that shows the relationship of 40%, X, and 35.

Use your equation to find x. Show your reasoning

Answers

Answer:

87.5

Step-by-step explanation:

-2/7x - 11 + 4/7x - 7

Answers

Answer:

2/7x - 18

Step-by-step explanation:

-2/7x - 11 + 4/7x - 7

rearrange the expression so it's easier to add, optional

-2/7x + 4/7x - 11 - 7

2/7x - 18

Use the linear equations to answer the question.
y=2/3x-3
y=-3/2x+2
Which statement about the lines is true?

Answers

Answer:

c. the lines are perpendicular.

Step-by-step explanation:

James has 165 centimeters of yarn left. How many inches does he have left?
(1 inch = 2.54 centimeters).

Answers

Answer:

64.96 inches

Step-by-step explanation:

this is because calculations excuse length value by dividing by 2.54

165/ 2.54 = 64.96 inches

PLEASE HELP ME WITH THIS. 5 POINTS

Answers

Answer:

I think b is not proportional

What is the slope of a line going through these 2 points? Point 1: (12,16) Point 2: (34 , 49)​

Answers

Answer:

1.5

Step-by-step explanation:

Please help I have ten minutes

Answers

Answer:

$10 per hour

Step-by-step explanation:

As you can see, at (2, 20) the employee earns 20 dollars for 2 hours and at   (4, 40) we can see the employee earn $40 per 4 hours.  So we can find the slope of these two points to get the answer.

Slope formula y1-y2/x1-x2

so plug it in    

40-20/4-2 and we get 20/2 =10

The midpoint of \overline{\text{AB}}AB is M(-6, -4)M(−6,−4). If the coordinates of AA are (-4, -3)(−4,−3), what are the coordinates of BB?​

Answers

Answer:

The coordinates of B is (-8,-5).

Step-by-step explanation:

The midpoint of line AB is M. The coordinate of M is (-6,-4).

The coordinates of A is (-4,-3)

We need to find the mid point of B.

If M(x,y) is the midpoint of the coordinates (x₁,y₁) and (x₂,y₂). The mid point theorem is used as follows :

[tex]M(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

Let the mid point of B is (x₂,y₂). Put (x,y) = (-6,-4), (x₁,y₁) = (-4,-3).

[tex](-6,-4)=(\dfrac{-4+x_2}{2},\dfrac{-3+y_2}{2})\\\\\dfrac{-4+x_2}{2}=-6\ \text{and}\ \dfrac{-3+y_2}{2}=-4\\\\-4+x_2=-12\ \text{and}\ -3+y_2=-8\\\\x_2=-12+4\ \text{and}\ y_2=-8+3\\\\x_2=-8\ \text{and}\ y_2=-5[/tex]

So, the coordinates of B is (-8,-5).

The coordinates of B are (-8, -5).

Given that,

The midpoint of AB is M(-6, -4). If the coordinates of A is (4,-2),

We have to determine,

The coordinates of B.

According to the question,

The midpoint of line AB is M. The coordinate of M is (-6,-4).

And the coordinates of A is (-4,-3)

If M(x, y) is the midpoint of the coordinates (x₁, y₁) and (x₂, y₂). The midpoint theorem is used as follows :

[tex]M(x, y) = ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

Let the midpoint of B be (x₂, y₂).

M (x, y) = (-6,-4), and (x₁, y₁) = (-4,-3).

[tex]M(-6, -4) = ( \dfrac{-4+x_2}{2}, \dfrac{-3+y_2}{2})\\\\[/tex]

Solving the equation for the co-ordinate B.

[tex]\dfrac{-4+x_2}{2} = -6\\\\-4 + x_2 = -6 \times 2\\\\-4 + x_2 = -12\\\\x_2 = -12+4\\\\x_2 = -8[/tex]

And,

[tex]\dfrac{-3+y_2}{2} = -4\\\\-3 + y_2 = -4 \times 2\\\\-3 + y_2 = -8\\\\y_2 = -8 + 3\\\\y_2 = -5[/tex]

Hence, The required coordinates of B are (-8, -5).

To know more about Geometry click the link given below.

https://brainly.com/question/20261153

Determine if each function is linear or non linear.

y = x/2 - 19,
3y = x^2,
13y = 1/3x + 5,
y = x + 25/5
y^3 = x

Answers

Answer:1)Linear 2)Non linear 3)Linear 4)Linear 5)Non linear

Step-by-step explanation:

If x is alone with no degree, it’s linear.

If b= 3, then b-2 is equivalent to

Answers

Answer:

1

Step-by-step explanation:

son

Use the substitution method.

b-2

3-2

= 1

Answer :

1

Answer this please thanks

Answers

Answer:

D. 182.4

Step-by-step explanation:

0.48 x 380 = 182.4

182.4
NEVER multiply a percent! Change it into a decimal.
.48x380

Why are whole numbers rational numbers? Use 15 as an example.

Answers

Answer:

Every whole number n can be written as a fraction of integers.

Step-by-step explanation:

Every whole number n can be written as a fraction of integers: x=x/1.

If we use 15 as an example, it would be 15 = 15/1. 15/1 is 15.

So whole numbers are rational

Whole numbers are rational numbers because all whole numbers can be expressed in the form a/b. Hence, 15 can be expressed as a rational fraction thus 15/1

When a number can be expressed in the form a/b ; such that the value of the denominator, b ≠ 0 ; then the number is said to be rational.

Whole numbers are positive integer values and as such, they are not decimals.

Every whole number can be expressed such that the denominator is 1 ; hence, they can be expressed in the form a/b.

15 as a whole number can be rewritten as 15/1. Hence, all whole numbers are rational.

Learn more : https://brainly.com/question/18109354

Simplify:

7r + 10 - 2(2r + 3s - 5t) + 2(4s - t) + 5 *

Answers

Answer:

3r+2s+8t+15

Step-by-step explanation:

After simplifying 7r+10-2(2r+3s-5t)+2(4s-t)+ 5, you will have 3r+2s+8t+15.

I dont know how to dis um can yalls help me yalls are so nice for helping me thx

Answers

Answer:

5 gallons

Step-by-step explanation:

5 gallons np bro good luck


Solve the system:

x=49-5y
x=16-2y

Write down the solution.

Answers

49 - 5y = 16 - 2y
49 = 16 + 3y
33 = 3y, y = 11
x = 49 - 5(11)
x = 49 - 55, x = -6
Solution: x = -6, y = 11

Which fractions are equivalent to 1/8+5/8? Check all that apply.

Answers

The equivalent fractions are 3/4 & 12/16 hope this helps!!

Answer:

3/4 and 12/16

Step-by-step explanation:

[tex]\frac{1}{8} +\frac{5}{8} =\frac{1+5}{8} =\frac{6}{8} =\frac{3}{4} \\\\\frac{12}{16} =\frac{3}{4}[/tex]

What is the magnitude of the vector shown?
5
13
radical 5
radical 13

Answers

Answer:

D on edge

Step-by-step explanation:

radical 13

g E. (i). An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that the first strike comes on the third well drilled

Answers

Answer:

0.128

Step-by-step explanation:

Given that :

Probability of striking oil = p = 20% = 0.2

Striking occurs on the 3rd well drilled : x = 3

Hence ;

P(x = 3) =?

Using a geometric probability function :

p(x = x) = (1 - p)^(x - 1) * p

P(x = 3) = (1 - 0.2)^(3 - 1) * (0.2)

P(x = 3) = 0.8^2 * 0.2

P(x = 3) = 0.64 * 0.2

P(x = 3) = 0.128

urgent answer please!!! :)

Answers

Answer:

a and b are relative on maxima interval x =-4,x=0

how much is left from 50 after buying 3 books at $
12.65 each​

Answers

Answer:$12.05

Step-by-step explanation:

12.65*3=$37.95

$50-$37.95=$12.05

please help with right answers​

Answers

The answer is 25.

4 green balloons : 5 purple balloons
20 green balloons : 25 purple balloons.

In order to get to 20 from 4 u need to multiply by 5. Do that to each side and get 25

Answer:

25

Step-by-step explanation:

the ratio is 4:5

20/4=5

so multiply 5 by 5 and you will get 25

on the number line jump to where it shows the very end where 20 is and at the bottom it is 25

hope that helps

I desperately need the answers to this, it’s about compound interests

Answers

Answer:

quarterly is n = 4semiannually is n = 2monthly is n = 12annually is n = 1

Step-by-step explanation:

n is the number of times the interest is compounded, so just figure out stuff like monthly and annually mean. (ex. since annually means once a year, n = 1)

Mike is 5 years old and Randy is 8 years old. Select the proportional relationship that has the same ratio to that of Mike and Randy's age.

Answers

5:8
mike is 5:randy is 8
5:8 mike being 5 and Randy being 8

The point R(-3,a,-1) is the midpoint of the line segment jointing the points P(1,2,b)
and Q(c,-7,4)
Find the values of:
a=
b=
C=

Answers

Answer:

The values are:

a = -5/2

b = -6

c = -7

Step-by-step explanation:

Given

P = (x₁, y₁, z₁) = (1, 2, b)  

Q =  (x₂, y₂, z₂) = (c, -7, 4)  

As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b)  and Q(c,-7,4), so

m = R = (x, y, z) = (-3, a, -1)

Using the mid-point formula

[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]

given

(x₁, y₁, z₁) = (1, 2, b) = P

(x₂, y₂, z₂) = (c, -7, 4) = Q

m = (x, y, z) = (-3, a, -1) = R

substituting the values in the mid-point formula

[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]

[tex]\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]

as (x, y, z) = (-3, a, -1), so

[tex]\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]

so solving 'c'

-3 = (1+c) / (2)

-3 × 2 = 1+c

1+c = -6

c = -6 - 1

c = -7

solving 'a'

a = (2+(-7)) / 2

2a = 2-7

2a = -5

a = -5/2

solving b

-1 = (b+4) / 2

-2 = b+4

b+4 = -2

b = -2-4

b = -6

Thus, the values are:

a = -5/2

b = -6

c = -7

Verification:

[tex]\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]

[tex]\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]

put a = -5/2, b = -6, c = -7

[tex]\left(-3,\:-\frac{5}{2},\:-1\right)\:=\:\left(\frac{1+\left(-7\right)}{2},\:-\frac{5}{2},\:\frac{\left(-6\right)+4}{2}\right)[/tex]

[tex]\left(-3,\:-\frac{5}{2},\:-1\right)\:=\:\left(\frac{-6}{2},\:-\frac{5}{2},\:\frac{-2}{2}\right)[/tex]

[tex]\left(-3,\:-\frac{5}{2},\:-1\right)\:=\:\left(-3,\:-\frac{5}{2},\:-1\right)[/tex]

volcano Puu Puai in Hawaii was formed in 1959 when a massive “lava fountain” erupted. The lava shot from the ground with an initial velocity of 350 feet per second.
a. For how long was the lava in the air until it returned to the ground?
b. What was the maximum height of the lava?
c. After how many seconds did the maximum height occur?

Answers

Answer:

a)Tt = 21,41 s

b) y(max) = 1873 ft

c)  t = 10,70 s

Step-by-step explanation:

We assume that this is a case of vertical shooting then:

a) Vf  = V₀  -  g*t

Vf = 0         -g*t = -V₀

t  =  V₀ /g         t  =  350 ft/s / 32,7 ft/s²

t  =  10,70 s     time for lava to reach y maximum

a) Then  Tt = 2*10,7     Tt = 21,41 s

Lava was in the air for  Tt = 21,41 s

b) y = y₀ + v₀*t - (1/2 )*g*t²

for y = ymax  we get:

y(max)  = 0 + 350*10,70 - 0,5* 32,7* ( 10,70)²

y(max)  =  3745  - 1872

y(max) = 1873 ft

c) t = 10,70 s

Need answer asap pls..............

Answers

Answer:

These go up by 1.

Step-by-step explanation:

10 20 30 40 50 60 70 80 90

1 + 1 = 2

2 + 1 = 3

3 + 1 = 4, and so forth.

Answer:

A (they go up by one )

Step-by-step explanation:

10, 20 , 30 ,40,50 The tens place goes up by  1 each time

Other Questions
Consulting a doctor, choosing the correct clothes, and using appropriate protective equipment are all important steps in beginning an exercise program.Please select the best answer from the choices provided.TF Find the fifth term in the geometricsequence, given the first term andthe common ratio.a1 = 2 and r = 3a5 = [ ?] How did President Putin demonstrate Russias growing military power? A. invading Afghanistan B. rebuilding nuclear weapons C. going to war with Iran D. defeating rebels in Chechnya CAN ANYONE WRITE A PARAGRAPH EXPLAINING ABOUT ANCIENT SPORTS In the triangle below, what is the length of BC The men go / goes to office daily Please help to anyone who is good with maps/geography i'm having trouble seeing that map and its confusing for me Q: In an examination 14% of the students failed and 559 students passed. Findthe number of students who failed? An amusement park is considering installing an outdoor ice-skating rink, which costs $950,000. Expenses for operating and maintaining the ice-skating rink are estimated at $2,500 each day it is used. The outdoor skating rink can only be used when the weather is sufficiently cold, so its usage is limited. The US weather service estimates that there is a 50% probability of 80-day suitable weather per year, 30% probability of 100 days per year, and 20% probability of 120 days per year. The operators of the amusement park estimate that during the first 80 days of use in a season, an average of 500 people will skate each day, at a fee of $20 each. If 20 additional days are available, the rink will be used by only 400 people each day during the extra period, and if 20 more days of skating are available, only 300 people per day will use the rink during those days. The management of the amusement park wish to recover any invested capital within three years and want at least a 22% per year rate of return before taxes. Based on before tax analysis, should the outdoor ice-skating rink be installed Companies that are concerned with boosting workplace morale, maximizing employees' productivity and creativity, and motivating employees to be more effective are concerned with:_______a. human relations b. behavior modification c. sustainability d. control systems e. workplace capacity ____determine the carrying capacity of an environment for a species.HELP PLEASE Once you stop the charge, how will you defeat (kill) the knights? They wear heavy armor! In order to estimate the number of monkeys living in a certain rain forest, Finn catches 90 monkeys, marks them, and releases them. Later, Finn catches 550 monkeys and notes that 50 of them are marked. To the nearest whole number, what is the best estimate for the monkey population? QUICK: life on earth is greatly impacted by photosynthetic organisms. what do such organisms contribute to living organisms? CAN SOMEONE PLEASE SEND THERE ESSAY FOR "Writing a Convincing Argument" ON EDGENUTY WORTH 25 THICC POINTS fox's diploid number of chromosomes is 36. How would the number of chromosomes in the fox's body cells compare to the number of chromosomes in its gametes? Ms. Harmon is a teacher with 28 students. Every school day, Ms. Harmon prints out 2 pages of worksheets for each of them. There are 81 school days left in this school year. Ms. Harmon works out that she will need to print a total of 137 pages in this time. Does that sound about right?Yes No it is much low No it is much high 20 points, please help I really bloody need it2. The equation x+2= v-----3x+10 is of the form x+a=v------bx+c ,where a, b, and c are all positive integers and b>1. Using this equation as a model, create your own equation that has extraneous solutions. (a) Using trial and error with numbers for a, b, and c, create an equation of the form x+a=v-----bx+c, where a, b, and c are all positive integers and b>1 such that 7 is a solution. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.) (b) Solve the equation you created in Part 2a. (c) If your solution in Part 2b did not have an extraneous solution, revise your equation so that 7 is one solution and there is an extraneous solution. If your solution in Part 2b did have an extraneous solution, create another equation with different values of a, b, and c that also has 7 as one solution and an extraneous solution. What is the solution set for this quadratic equation 2(x-3)^2-4=28 Please help on timer ill give 15 brainlist