Find the equation of a parabola in vertex form with given vertex and point.
Vertex (0,1) and passing through (-1,0)

Answers

Answer 1

keeping in mind that we could have a horizontally opening parabola or a vertically opening one using those values, let's use the vertical parabola type for the equation

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(0,1)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]y=a(x-0)^2+1\implies y=ax^2+1\qquad \textit{we also know that when} \begin{cases} x = -1\\ y = 0 \end{cases} \\\\\\ 0 = a(-1)^2+1\implies 0=a+1\implies \boxed{-1=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-x^2+1\implies \stackrel{\textit{vertex form}}{y = -(x-0)^2+1}~\hfill[/tex]


Related Questions

Find the difference (10j-7)-(-9j+2)

Answers

Answer:

19j-9

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

10+9=19j

-7-2=9

These triangles
are congruent by
the triangle
congruence
postulate [? ].
A. ASA
B. Neither, they are not congruent
C. AAS

Answers

Since in the two triangles,

2 angles and the side between them is given and equal, the triangles are congruent using the Criteria ASA.

Option A is the correct answer.

2/3x−1/6y=1/2

2x – 4y = 3

Answers

Answer:

30

Step-by-step explanation:

3x+6y=9

multiply by 2

6x+12y=18   ....(1)

-2x+-4y=4

multiply by 3

-6x-12y=12   ...(2)

add (1) and (2)

0+0=30

express 1 000 000 in standard form

Answers

Answer:

10^6.

Step-by-step explanation:

There are 6 digits after the 1 so it's 1 * 10^6 or just 10^6.

what are five example recurring decimal

Answers

Answer:

These are some examples of recurring decimals.

Definiton:

A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero.

Evaluate. 10/1·(−4) Enter your answer in the box.

I’ll give brainliest if its correct on the test! (And if i can figure out how)

Answers

Step-by-step explanation:

10/1(-4)

10(-4)

=-2.5 or 5/-2

Please help!!

1) Mark a central angle and calculate the measure of the central angle in the polygon below. *

Answers

Answer:

the measure of the central angle of a regular nonagon is 40 degrees.

In a movie's opening weekend, 879,575 tickets are sold in 755 theaters. The average cost of a ticket is $9.50. What is the average amount of money earned by each theater?

Answers

The anwser 1,165. !!

Answer:

$11 067.50 each theater

Step-by-step explanation:

879575 * 9.50 = 8355962.50 revenue total   8355962.50 / 755 = $11 067.50 each theater

1. find measure of A.

2. find measure of B.

3. find measure of C

4. find measure of D

pls give picture and explanation

Answers

Answer:

Measure of angle A = 120°

Measure of angle B = 98°

Measure of angle C = 104°

Measure of angle D = 140°

Step-by-step explanation:

Find measure angle A :-

Since the two straight lines are parallel

, then A + 12X =180° (alternate angles)

, then A = 180° - 12X

Since the two straight lines are parallel

, then measure angle A = measure angle (25X-5)°

(opposite angles)

, then 180° - 12X = 25X - 5° (solve it like a normal equation)

, then 180° + 5° = 25X + 12X

, then 185° = 37X

, then X = 185° ÷ 37

= 5

, then measure of angle A = 180° - ( 12 x 5 )

= 180° - 60°

, then measure angle A = 120°

Find measure angle B :-

Since the two straight lines are parallel

, then measure angle B = measure angle 14X (corresponding angles)

, then 15X - 7 = 14X

, then 15X - 14X = 7

, then X = 7

Since X =7

, then measure angle B = (15 x 7) - 7

= 105° - 7

, then measure angle B = 98°

Find measure angle C :-

Since the two straight lines are parallel

, then measure angle C = 8X

(opposite angles)

, then 5X + 39 = 8X

, 39 = 8X - 5X

, 39 = 3X

, then X = 39 ÷ 3

, X = 13

Since X = 13

, then measure angle C = (5 x 13) +39

= 65 + 39

, then measure angle C = 104°

Find measure angle D :-

Since straight that angle D lies on = 180°

, then sum of measure of and D and 4X =

180°

, then (12X + 20) + 4X = 180°

, then 16X + 20 = 180°

, then 16X = 160° (resulting from 180° - 20°)

, then X = 10

Since X = 10

, then 12 x 10 + 20 = 120 + 20

,the measure angle D = 140°

Angle ABC and angle BD are complementary.

The measure of angle ABC equals (3x + 4) degrees, and

the measure of angle CBD equals (5x +6). Find the measures of both angles.

Answers

Answer:7x

11x

Step-by-step explanation:

PLEASE HELP

What is the value of the expression 12+23b when b=−5 ?

−176

−16

236

I don't know.

Answers

Answer: -103

Step-by-step explanation:

substitute in the value of B

12+23(-5)

multiply 23 and -5 together

12-115

solve

-103 is the answer

Answer:

-103

Step-by-step explanation:

What is the slope of the line created by this equation?
y = 10x+6

I need help getting started how do you do this

Answers

Answer:

Step-by-step explanation:

Well the answer is explained below.

What will it cost to carpet a rectangular floor measuring 21 feet by 9 feet if the carpet costs $31. 29 per square yard?

Answers

Answer:

$657.09

Step-by-step explanation:

The area of the carpet is:

21 × 9 = 189 Square foot

189 foot² = 21 yard²

We know 1 yard² = $31.29

So 21 yard² = 21 × $31.29 = $657.09

epic gamer question i'll mark brainliest​

Answers

Answer:

I think it is parallel

Step-by-step explanation:

Solve 2/v + 1/w = 1/2 for v

Answers

Answer:

v=(-4w)/(-w+2)

in which country has involved in world war

Answers

Answer:

The following countries were involved in the world war

Germany

Austria-Hungary

Bulgaria

Ottoman Empire (the Central Powers)

These countries fought against

Great Britain

France

Russia

Italy

Romania

Japan

United States (the Allied Powers).

Cheryl is planning to spend $75 on a Christmas gift for her father. He needs new socks and ties. A store has socks s and ties t on sale for $4 and $11, respectively. Which equation models this situation?

Answers

Answer:

4s + 11t = 75

Step-by-step explanation:

Assuming you are asking for an equation to find how many socks and ties Cheryl could get with $75, then the equation 4s + 11t = 75 would represent that.

s is the number of socks that are bought (assuming s = 1 means that 1 pair of socks is bought).

t is the number of ties that are bought.

4s represents the total cost of the socks that are bought (if you plug in 4 for s, then the total cost of the socks is 4(4) = 16+

11t represents the total cost of the ties that are bought

What is the equation of the line that passes through the point (-3,4)(−3,4) and has a slope of 11?

Answers

Answer:

y=5x-11 is the equation of the required line

72 boxes sold out of 90 boxes what percent sold

Answers

Answer:

80%

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

90 boxes = 100%

72 boxes = ?

=> (72 * 100)/ 90 = 80%

Please please help please help me help help me please help me

Answers

Step-by-step explanation:

-2 is x1

9 is y1

4 is X2

-1 is y2

m= -1-9/4-(-2)

-10/6 =-1.6

Tim has 2/3 cup of chocolate syrup. If he uses 1/9 cup of chocolate syrup for each serving of chocolate milk, how many servings of chocolate milk can he make

Answers

Answer:

6 servings

Step-by-step explanation:

Each serving Tim uses 1/9 cup. So, after using the amount of syrup reduces and repeated subtraction is division.

[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{9}[/tex]

[tex]=\dfrac{2}{3}*\dfrac{9}{1}[/tex]

= 2 *3

= 6


URGENT!!! Will MARK BRAINLIEST!!!
Select the correct answer.
What is the next step in solving this augmented matrix using the Gauss-Jordan elimination method?

OA.
Convert the matrix to the linear system form.
OB.
Divide R2 by 2 and R3 by 3.
OC.
The matrix is solved.
D.
This is an inconsistent matrix that cannot be solved.
O E.
Divide R1 by 2 and R3 by 3.

Answers

Answer:

B is the correct answer. I just took the test :))

Step-by-step explanation:

Option B is correct, Divide R₂ by 2 and R₃  by 3 is the  next step in solving this augmented matrix using the Gauss-Jordan elimination method.

In the Gauss-Jordan elimination method, the goal is to transform the augmented matrix into row-echelon form and then into reduced row-echelon form to solve the system of linear equations.

To achieve this, we perform row operations on the matrix.

In the given augmented matrix:

[tex]\left[\begin{array}{ccc}1&0&0\\0&2&0\\0&0&3\end{array}\right] .\left[\begin{array}{c}5&8&9\end{array}\right][/tex]

We can divide R₂ (Row 2) by 2 and R₃ (Row 3) by 3 to simplify the matrix further we do this to make the leading coefficient (the number at the leftmost position in each row) of each row equal to 1, which is a requirement for row-echelon form.

After dividing R₂ by 2 and R₃ by 3, the augmented matrix becomes:

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] .\left[\begin{array}{c}5&4&3\end{array}\right][/tex]

To learn more on Matrices click:

https://brainly.com/question/28180105

#SPJ2

Line ℓ has equation y=5. Find the distance between ℓ and the point Q(0,1).

Answers

Answer:

Distance = 4

Step-by-step explanation:

Given the linear equation of line ℓ, y = 5 which is a horizontal line in which its slope, m = 0 (zero slope), and each of the x-coordinates along the line have the same y-coordinate of y = 5.

In order to determine the distance of the horizontal line from the given point Q, (0, 1), use the following distance formula:

[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]

Choose any x-coordinate to pair with the y-coordinate, y = 5. Let's use the y-intercept, (0, 5).

Let  (x₁, y₁) = (0, 1)  

      (x₂, y₂) = (0, 5)  

Substitute these values into the distance formula:

[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]

[tex]d = \sqrt{(0 - 0)^{2} + (5 - 1)^{2}}[/tex]  

[tex]d = \sqrt{(4)^{2}}[/tex]

[tex]d = \sqrt{16}[/tex]

d = 4  

Therefore, the distance of line ℓ from point Q is 4.

Question 10 of 10
Which of the following is the solution to the inequality below?
-2/6(4-x)<4(x+1/2

Answers

Answer:

x > -11/10

Step-by-step explanation:

-2/6(4-x) < 4(x+1/2)

-1/3(4-x) < 4x + 2

-4/3 + 1/3x < 4x + 2

-4 +x < 12x + 6

x - 12 x < 6 + 4

-11x < 10

x > -11/10

420 is divided between george and Nancy in the ratio 2:3 Find who get more money.​

Answers

Answer:

Nancy gets more, she gets 252 while George gets 168.

Step-by-step explanation:

420÷5=84

168:252

George:Nancy

if a 1x1 foot tile costs 3.50 each ,how much will it cost mr teal?

Answers

Answer:

Hope this helps.

Step-by-step explanation:

When measuring for floor tile the rule is:

Length x Width + Waste = Amount Needed

Waste Factor will vary based upon tile size, layout, configuration of room, patterns, etc. Typical waste factor is about 10%. Add 15% for tile being installed diagonally or for a room with lots of jogs and corners. These installations will require more cuts and thus more waste.

HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Answers

Answer:

HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

PLEASE HELP DUE NOW!!!
WILL MARK BRAINLIEST!!!!

Answers

Answer:

In point form, the answer is (1, -7) and in equation form, x = 1, y = -7.

Step-by-step explanation:

I hope this helps!

Solve 8T 1398lb 14oz * 6

Answers

this is soo funny

haha thanks for the points

four and three sevents plus six and one fith.

Answers

372/35 or 10.62857143
You could find a common denominator or use a calculator
Other Questions
which group has the power to advise and consent on some executive decisions?A. senate B. supreme court C. house of representatives The final scores of students in mathematics are distributed normally with a mean of 72 and a standard deviation of 10. What is the probability that a students score will be between 65 and 78?. hello! someone please answer this. this is due tomorrow, Monday and I don't get any of it. ty! You place a small sphere with a net charge of 5 space x space 10 to the power of negative 6 end exponent space C at one corner of a square that measures 5 m on each side. What is the magnitude of the electric field at the opposite corner of the square?900 N/C9,000 N/C450 N/C4,500 N/C Which part of an apple best represents Earth's crust? (3 points)FleshSeedSkinStem Write the numbers below in orderfrom least to greatest.1.4 10.4 1.45 1.54 10.54 *HIGH SCHOOL* please help me with this what is the 4 digit code? This is urgent please help I give brainliest if right Did the Supreme Court rule in favor of Plessy? The use of words that sound like the things they stand for, such as "buzz" and "hiss", is known as Determine the force required to move a block if the coefficient of static friction of one block and the floor is 0.35 and the coefficient of the static friction between 2 boxes is 0.25 me pueden decir que palabras son verbos comprar vaya tomate calmaropa compraventa tomate es Baker leaves his house and drives 10 miles north then 24 miles west to Tellus Science Museum. IfBaker could drive in a straight line from his house to the museum, how many miles would he save?How many miles is the normal route?How many miles is the straight line?How many miles would Baker save? (Hint: subtract the two.) A conversation that focused on the feelings and thoughts of the participants would be most appealing to a ___________________ listener.a.action-orientedb.people orientedc.time-orientedd.content oriented The length of a rectangle is 2 inches more than its width. The area of the rectangle is equal to 12 inches more than three times the perimeter. Find the lengthand width of the rectangle. Elie in night believes that remembering theHolocaust will help ensure that this typeof atrocity does not occur in the future.Do you think learning about historicalevents can guide people to behavedifferently? Explain. How many solutions can be found for the system of linear equations represented on the graph?A) no solutionB) one solutionC) two solutionsD) infinitely many solutions evaluate 102 what is the answer exhibiting a personality that ________ is a common characteristic of all personality disorders.