Mathematics College

Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.(h, k) = (1, 0), (x, y) = (0, 1)f(x) =

Answers

Answer 1

A quadratic equation can be written in the vertex form to be:

$y=a(x-h)^2+k$

where (h, k) is the vertex.

The question gives the following parameters:

$\begin{gathered} (h,k)=(1,0) \\ (x,y)=(0,1) \end{gathered}$

We can use these values to solve for a:

$\begin{gathered} 1=a(0-1)^2+0 \\ a=1 \end{gathered}$

Therefore, the vertex form of the quadratic equation will be:

$y=(x-1)^2$

Expanding, we have the general form of the quadratic equation to be:

$f(x)=x^2-2x+1$

Related Questions

Hosting a dinner party for 38 people, you plan to serve peach pie for desert.
Each pie has 8 slices.
How many slices are in each pie?

Answers

Answer:

40 slices

Step-by-step explanation:

I rounded 38 to 40 and divided by 8

what is the kinetic energy of 1500 kg pick-up truck traveling at 31.0 m/sec.

Answers

The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.

What is kinetic energy?

If the body of the mass (m) is moving with a velocity (v), then the body possesses the energy which is known as kinetic energy. The SI unit of the kinetic energy is Joule. Then the formula is given as,

KE = 1/2 x mv²

The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec is given as,

KE = 1/2 x 1500 x 31²

KE = 720,750 Joule

KE = 720 kJ

The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.

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Find the nth term of this quadratic sequence
2,8, 18, 32, 50,

Answers

Answer:

Step-by-step explanation:

8 = 2×2^2

18 = 2×3^2

32 = 2×4^2

50 = 2×5^2

72 = 2×6^2

Can anyone help me please ????

Answers

Hey there! The topic for this problem is Limit of Function!

As for the question, we are given the quadratic function and we have to find the limit, the value that approaches to a.

$ \large \boxed{lim_{x \longrightarrow a} f(x)}$

We call this, "The limit of f(x) when x approaches a."

Then you may ask, "How do we find the limit of function?". That is a very nice question! The answer to your problem is just substitute x-value in. Although this substitution method only applies when the approaching value doesn't make the denominator to 0. I believe that in the beginning of Limit topic, we learn how to find or evaluate the basic limit that only requires substitution.

So from the question, we receive:

$ \large{lim_{x \longrightarrow 2} ( {x}^{2} - 3x - 1)}$

Next step is to substitute x = 2 in the function.

$ \large{lim_{x \longrightarrow 2} ( {2}^{2} - 3(2) - 1)}$

Evaluate the value.

$ \large{lim_{x \longrightarrow 2} ( 4 - 6 - 1)} \\ \large{lim_{x \longrightarrow 2} ( - 3)}$

Cancel the limit out and there you have it!

$ \large \boxed{ - 3}$

Answer

The limit of quadratic function when x approaches 2 is -3.

Now whenever you learn limit, you must know that limit is when we substitute the approaching value. That means x —> 2 is not x = 2 but x approaches 2.

Regarding the limit, any questions and doubts can be asked through comment and I will get back to you soon!

Thank you for using Brainly and I hope you have a fantastic day! Good luck on the assignment.

Aaliyah has a loyalty card good for a discount at her local hardware store. The item she wants to buy is priced at $39, before discount and tax. After the discount, and before tax, the price is $33.54. Find the percent discount.

Answers

Answer:

14 % discount

Step-by-step explanation:

Item she wants to buy is priced at $39

After the discount, and before tax, the price is $33.54.

39.00 x .14 = 5.46

39.00 - 5.46 = $33.54

Answer:

16.13

Step-by-step explanation:

The hanger image below represents a balanced equation.

Answers

Answer:

$ \frac{1}{5} + z = \frac{3}{5} $

Answer:

1/5+z=3/5

Step-by-step explanation:

Please awnser asap I will brainlist

Answers

The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

How to obtain the union and intersection set of two sets?

The union and intersection sets of multiple sets are defined as follows:

The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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marco set aside 50 minutes

Answers

Answer:

So what's the Question Because to me it looks like something random

3.663 to the nearest tenth of a ounce

Answers

Answer:

3.7 ounces

Step-by-step explanation:

You just need to round to nearest 10th place, which is just next number after decimal. Hope it helps ;)

income from operations of $231,000. In addition, it received interest income of $23,100 and received dividend income of $29,700 from another corporation. Finally, it paid $11,000 of interest income to its bondholders and paid $45,000 of dividends to its common stockholders. The firm's federal tax rate is 21%. What is the firm's federal income tax? Do not round intermediate calculations. Round your answer to the nearest dollar.

Answers

The firm's federal income tax is $57,168.

To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.

In this case, the firm's total income consists of income from operations, interest income, and dividend income.

Total income:

Income from operations = $231,000

Interest income = $23,100

Dividend income = $29,700

Total income = $231,000 + $23,100 + $29,700 = $283,800

Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:

Total expenses = Interest paid to bondholders = $11,000

Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800

Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:

Federal income tax = Taxable income * Federal tax rate

Federal income tax = $272,800 * 0.21 = $57,168

Therefore, the firm's federal income tax is $57,168.

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what are the features of the function g if g(x)= f(x+4) +8

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The domain, range, x-intercept, or y-intercept of g(x) = f(x + 4) + 8. The features of g depend on the corresponding features of f.

Given the function g(x) = f(x + 4) + 8, let's examine its features:

Domain:

The domain of the function g will be the same as the domain of the function f, which depends on the restrictions or constraints of f. However, it is important to note that shifting the input by 4 units (x + 4) does not inherently change the domain unless there are specific restrictions imposed by f.

Range:

Similar to the domain, the range of the function g will depend on the range of the function f.

x-intercept:

The x-intercept of a function is the point where the graph intersects the x-axis, meaning the y-coordinate is zero (y = 0). To find the x-intercept of g(x), we set g(x) = 0 and solve for x.

0 = f(x + 4) + 8

By subtracting 8 from both sides:

-8 = f(x + 4)

Since the exact value of x that makes f(x + 4) equal to -8. The x-intercept will depend on the behavior of f.

y-intercept:

The y-intercept of a function is the point where the graph intersects the y-axis, meaning the x-coordinate is zero (x = 0). To find the y-intercept of g(x), we substitute x = 0 into the function:

g(0) = f(0 + 4) + 8

g(0) = f(4) + 8

Again, the specific value of f(4) will depend on the behavior of the function f.

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i had it wrong it said A&C

Answers

Answer:ez

Step-by-step explanation:

you had what wrong? what was the question :)

11 of 3011 of 30 Questions

Question
A baker makes peanut butter cookies and chocolate chip cookies.

She needs 2 cups of flour and 34
cup of butter to make one batch of peanut butter cookies.
She needs 3 cups of flour and 1 cup of butter to make one batch of chocolate chip cookies.
If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?

Answers

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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Naomi has a lot of stuff in her pencil case. There are 18 items in her pencil case, including 9 pencils. What is the probability that a randomly selected item from Naomi's pencil case will be a pencil? Write your answer as a fraction or whole number. P(pencil) =

Answers

Answer:

p=1/2

Step-by-step explanation:

If 9 is 1 half of 18 that means there is a 50% chance of you picking a pencil out of the pencil case

Simplify the expression to a polynomial in standard form: (4x+5) (x^2-3x-2) PLEASE HLEP

Answers

Answer:

$4x^3-7x^2-23x-10$

Step-by-step explanation:

So we have the expression:

$(4x+5)(x^2-3x-2)$

Distribute. Multiply (4x+5) to each term:

$(x^2)(4x+5)+(-3x)(4x+5)+(-2)(4x+5)$

Distribute:

$=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)$

Combine like terms:

$=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)$

Add and simplify:

$=4x^3-7x^2-23x-10$

And this is in descending order, so it's in standard form.

dont now anwer on thesse 3 question

1:The sum of k and 85
2: 6 subtracted from t
3:The difference of 99 and 19 a, divided by 6

Answers

Answer:

$1.k + 85$

$2.t - 6$

$3. \frac{99 - 19}{6} or \frac{19 - 99}{6} $

i am very sure of the first and second but I have two of the options for the third.

I hope this helps!

If there are initially 5000 bacteria in a culture, and the number of bacteria triple each hour, the number of bacteria after t hours can be found using the formula y = 5000(3)^t. How long will it take the culture to grow to 80,000? Round to the nearest tenths.

Answers

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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If x = 8 units, y = 5 units, and h = 3 units, then what is the area of the parallelogram shown above?

Answers

Answer:

Area of Parallelogram Using Diagonals ; Using Base and Height, A = b × h ; Using Trigonometry, A = ab sin (x) ; Using Diagonals, A = ½ × d1 × d2 .....

Using Diagonals: A = ½ × d1 × d2 sin (y)

Using Base and Height: A = b × h

Using Trigonometry: A = ab sin (x)

You earn $42 for washing 7 cars. How much do you earn for washing one car? How much do you earn for washing 3 cars? How much do you earn for washing 5 cars?

Answers

Answer:

1 car = $6 ; 3 car = $18 ; 5car = $30

Step-by-step explanation:

$ 42 = 7 cars

so 1 car = $42÷7 = $6

so 3 cars = 3 × $6 = $18

so 5 cars = 5 × $6 = $30

Hope this helps you.

Calculate the difference and enter below. -4 + (-4)

Answers

$-4-4$

$-4+(-4)$

$=\fbox{-8}$

$-4+(-4)$ on a number line:

Calculate the difference and enter below. -4 + (-4)

Which expression has a sum of 42?

Answers

Answer: Sorry meant to send this*

Step-by-step explanation:

The point (2-4) is reflected across the line y=-1. What are the coordinates of the image?
A (5,4)
B. (4,2)
C. (2,2)
D.(2,4)

Answers

The correct answer to this question is C

Solve for q
1/p + 1/q= -1/f
where p + q = 3 and f=5

Answers

We can solve for q by first substituting the value of p from the second equation into the first equation:
1/p + 1/q = -1/f
1/(3-q) + 1/q = -1/5

Next, we can cross-multiply and combine like terms:
5 + 5q = -3 + 3q
8q = -8
q = -1

dillion took out a 2 year loan for $2375 at a sports -equment store to be paid back with monthly at a 6.6% APR compounded monthly if the loan offers no payments for the first 5 months, how much will dillion owe when he begins making the payments?

Answers

If the loan offers no payments for the first 5 months, the amount owed by Dillion when he begins making the payments is $2,441.03

What is the effective monthly interest rate on the loan?

The effective monthly interest rate on the loan is determined as the annual percentage rate(APR) of 6.6% divided by 12 months since there are 12 months in a year

effective monthly interest=6.6%/12

effective monthly interest=0.0055

FV=PV*(1+r)^N

FV=the balance owed after 5 months=unknown

PV=the loan amount=$2375

r=effectively monthly interest rate=0.0055

N=number of months that have passed since the loan was taken=5

FV=$2375*(1+0.0055)^5

FV=$2,441.03

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The height of Ahmed is 30 inches . Convert his height to centimeters

Answers

Answer:

height is 76.2 centimeters

Use the figure to find the product (x + 3)(x + 2). (Hint: Find the area of each small square or rectangle, then add.)

Answers

Answer:

2x×5

Step-by-step explanation:

x+x×3+2

2x×5

Will give Brainliest!
Find the period and amplitude of the function.
y = -4cos(4/3 x)
Give the exact values, not decimal approximations.

Answers

Answer:

y = d + a · cos(bx - c) ⇒ y = -4cos(4/3x)

a = -4b = 4/3c = 0d = 0

Amplitude = |a| = |-4| = 4

Period = $\frac{2\pi }{b} =\frac{2\pi }{\frac{4}{3} } =2\pi *\frac{3}{4} =\frac{3}{2} \pi$

Part 1 of 2
Evaluate the function f(x)=x-7 at the given value of the variable.
a. f(13)
b. f(3)

Answers

Answer:

b)-4

Step-by-step explanation:

a) f(13) = 13-7=

b) f(3)= 3-7= -4

Parametric Functions

Answers

Answer:

Step-by-step explanation:

it think it 23 becasue u add

1 divide it by 2

Part D
Now use GeoGebra to measure the lengths of segments AB and BC and calculate the area of rectangle ABCD. Do you get the same result that you obtained in part C? Take a screenshot with the lengths of the sides labeled and the area displayed, and paste it below.

Answers

Answer:

id ont givea

efijhaoieuvbhzoiubhoewivbawzoufhbealivjhbr

Step-by-step explanation:

idsifui piuh vSeth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity: