How would you find the quadratic that goes through the point (4,0), the axis of symmetry is x=7, and it also goes through the point (1,5)?

Answers

Answer 1

9514 1404 393

Answer:

  y = (5/27)(x -7)^2 -5/3

Step-by-step explanation:

Use the given points to find the unknowns in the equation.

If the axis of symmetry is x=7, then the equation can be written in the form ...

  y = a(x -7)^2 +b

Filling in the two point values, we have two equations:

  0 = a(4 -7)^2 +b   ⇒   9a +b = 0

  5 = a(1 -7)^2 +b   ⇒   36a +b = 5

__

Subtracting the first equation from the second, we have ...

  (36a +b) -(9a +b) = (5) -(0)

  27a = 5

  a = 5/27

Substituting that value into the first equation gives ...

  9(5/27) +b = 0

  5/3 +b = 0

  b = -5/3

So, the quadratic can be written in vertex form as ...

  y = (5/27)(x -7)^2 -5/3

How Would You Find The Quadratic That Goes Through The Point (4,0), The Axis Of Symmetry Is X=7, And

Related Questions

PLEASE HELP ASAP What part of 6 3/5 is 3 /10 ? PLS HELP ASAP

Answers

Answer:

the 3/5 part of 6 3/5

Step-by-step explanation:

3/5 is equal to 3/10 because when you find the common denominator of 10, you multiply 3/5 by 2 and 3/10 by 1 because 10 is already 10. 3/5*2=6/10.

Chloe bought three pounds of strawberries for $16.80. What is the price, in dollars per ounce of strawberries?

Answers

Answer:

$5.60

Step-by-step explanation:

Each pound of strawberries costs $5.60.

To solve: $16.80 divided by 3

Math 7 A Unit 4 lesson 2 Please help quick
5/10-3/10
1/2+3/4
1/6+3/8
7/8-5/12

Answers

Answer:

2/10, 1 1/4, 13/24, 11/24

Step-by-step explanation:

1. subtract the fractions

2. add the fractions

3. add the fractions

4. add the fractions

which is the product of 7/9 and 6 in a fraction number

Answers

Answer:

4 2/3

Step-by-step explanation:

7/9 multiplied by 6/1 = 42/9

Simplify: 14/3

Turn it into a mixed number: 4 2/3

Please I need help hurry!

Answers

Answer:

Step-by-step explanation:

Team B=2.2*4.8= 10.56

Team C : 10.56 *1.5=15.84

Hi can someone pls help me on the last question (#5)

Answers

[tex]solution \: (a) \:: [/tex]

[tex] \frac{1}{7} x = 1[/tex]

[tex]x = 7[/tex]

[tex] solution \: (b) \:: \\ x \times \frac{1}{11} = 1[/tex]

[tex]x = 11[/tex]

[tex]solution \: (c) \:: [/tex]

[tex]1 \div \frac{1}{5} = x[/tex]

[tex]x = 5[/tex]

Determine the number of real or non real solutions of the equation listed below
using the discriminant.
x2 + x + 4 = 0

Answers

Answer:

x =(-1+√-15)/2=(-1+i√ 15 )/2= -0.5000+1.9365i

Step-by-step explanation:

I got two answers

evaluate the​ expression, ​(g◦​f)(3​), given the following functions.
​f(x)=x+2 and ​g(x)=x

Answers

[tex]f(x) = x + 2\\g(x) = x\\(g \circ f) = g(f(x)) = x + 2\\g \circ f)(3) = 3 + 2 = 5[/tex]

-6(1/4x-2/3x+5/6x) simplified .

Answers

Answer:

[tex]-2\frac{-1}{2}[/tex]

Step-by-step explanation:

To distribute the -6, multiply every numerator by -6, this gets you

-6/4+12/3-30/6

To put these together, they all need to have a common denominator. We can make all of the denomiators 12 by multiplying the numerator by whatever we multiply the denominators by to get 12.

-18/12+48/12-60/12

This gets you -30/12

To make this a proper fraction, divide -30 by 12 and put the whole number to the left of the fraction (-2), making a mixed number. The remainder stays a fraction which is -6/12. This reduces down to -1/2. Put -2 and -1/2 together to get [tex]-2\frac{-1}{2}[/tex]

45 2/3 + 30 1/2 + 12 3/4=?​

Answers

88.9166666667.................

Write 0.6 as a percentage.

Answers

Answer:

60%

Step-by-step explanation:

all you need to do is multiply this by 100 (move two decimal places to the right).

0.6--> 60

60 percent

Answer: 60%

Explanation: .6 x 100 = 60

What is qualitative data? Give an example.

Answers

Answer:

it is data that you can see or describe such as he is a boy

Step-by-step explanation:

Find the distance between the points (-3, 5) and (7, -1), round the nearest 10th, if nessasary.

Answers

Answer:

The answer is 11.7 units

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3, 5) and (7, -1)

The distance between them is

[tex]d = \sqrt{ ({ - 3 - 7})^{2} + ({5 + 1})^{2} } \\ = \sqrt{( { - 10})^{2} + {6}^{2} } \\ = \sqrt{100 + 36} \: \: \: \: \: \: \: \\ = \sqrt{136} \\ = 2 \sqrt{34} \\ = 11.66190378...[/tex]

We have the final answer as

11.7 units to the nearest tenth

Hope this helps you

-3.5 , 2 , -3 , -1 , -1.5
Least to greatest

Answers

Answer:

-3.5, -3, -1.5, -1, 2

Step-by-step explanation:

Answer:

-3.5, -3, -1.5, -1, 2

Step-by-step explanation:

negatives to positives

How do you do this question?

Answers

Answer:

dy/dx = (2t + 3t²) / (2t)

Step-by-step explanation:

y = t² + t³

dy/dt = 2t + 3t²

x = 5 +t²

dx/dt = 2t

dy/dx = (dy/dt) / (dx/dt)

dy/dx = (2t + 3t²) / (2t)

How many squares are in the 11 squares

Answers

Answer:

11 Squares are there in 11 squares

Answer:

11

Step-by-step explanation:

because take your question and realize you put, "How many squares are in the 11 squares?"

(Sry if wrong or information misunderstood!)

B. A certain chocolate bar costs $50.00 per piece. However, if you buy more than
5 pieces they will mark down the price to P48.00 per piece. Use a piecewise
function to represent the cost in terms of the number of chocolate bars bought.​

Answers

Answer:

P(x) = $50.00*x     if    0 ≤ x ≤ 5

P(x) = $48.00*x     if     5 < x

Step-by-step explanation:

A piecewise function is a function that acts differently in different regions of the domain.

In this case we know that:

P = $50.00 per piece if the number of pieces is less or equal than 5.

P = $48.00 per piece if the number of pieces is more than 5.

Then if we define our variable x as the number of pieces of chocolate, we can write the price function as:

P(x) = $50.00*x     if    0 ≤ x ≤ 5

P(x) = $48.00*x     if     5 < x

Pls help me I will give out points

Answers

Answer:

A, the first one

Step-by-step explanation:

On the left side, the graph is going closer to 0, that explains the first coordinate 0. On the right side, the graph approaches positive infinity, so that explains the infinity. I hope this helps!

1/2 + 2 3/4

Help please (◍•ᴗ•◍)❤​

Answers

Answer:

3 1/4

Step-by-step explanation:

Answer:

3 1/4

Step-by-step explanation:

im going to change the fractions to decimals

1/2 = 0.5

2 3/4 = 2.75

0.5 + 2.75 = 3.25

now im going to switch it back to fraction

3.25 = 3 1/4

PLLSSSS HEELP


Solve and graph this absolute value equation.

|x – 2| – 8 = 7

Answers

Step-by-step explanation:

y-8=7 y=15

|x-2|=15 has two solutions

17,-13

Answer:

answer

(x_2)- 8=7

2x=8-7

2x=1

that's the answer

How is the sentence "8 less than y is 2" written as an equation?
A. 8-y = 2
B. y - 2 - 8
C. y - 8 - 2
D. y + 8 - 2

Answers

Answer:

y - 8 = 2

thats how you would write it so idk i guess pick c because its the closest

"8 less than y" ==> y-8

"is 2" ==> =2

therefore y-8=2

What transformation occurs to the graph f (x) =2x + 3 if the 3 in the equation is changed to a 5?

Answers

The equation will shift up two points

An account grows at an annual interest rate of r⁡​ ⁣, so it grows by a factor of x=1+r⁡​ ⁣⁣ ​⁡ each year. The function A(x)=800x 4 +350x 3 +500x 2 +600x⁣ ​⁡ gives the amount in the account after 4 years when the growth factor is x⁡​ ⁣⁣ ​⁡. What is the total amount in the account if the interest rate for the account is 3% each year? How much money was put into the account at the beginning?

Answers

Given:

Annual interest rate = r⁡​%

Growth factor : x = 1 + r⁡​

The below function gives the amount in the account after 4 years when the growth factor is x⁡​ ⁣⁣.

[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]

To find:

The total amount in the account if the interest rate for the account is 3% each year and initial amount.

Solution:

Rate of interest = 3% = 0.03

Growth factor : x = 1 + ⁡0.03 = 1.03

We have,

[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]

Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.

[tex]A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)[/tex]

[tex]A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609 )+618[/tex]

[tex]A(1.03)=900.407048+382.45445+530.45+618[/tex]

[tex]A(1.03)=2431.311498 [/tex]

[tex]A(1.03)\approx 2431.31 [/tex]

Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.

For initial amount the rate of interest is 0.

Growth factor : x = 1 + ⁡0 = 1

Substitute x=0 in the given function to find the initial amount.

[tex]A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)[/tex]

[tex]A(1)=800+350+500+600[/tex]

[tex]A(1)=2250[/tex]

Therefore, 2250 was put into the account at the beginning.

6/10 as hundredths in fraction form and decimal form

Answers

Answer:

60/100 and .6

Step-by-step explanation:

A school janitor has my 1/3 of the classroom in five minutes at what rate is he mopping

Answers

Answer:

1/15 per min

Step-by-step explanation:

3 times 5 equals 15 and so 1/15.

Try making a visual picture to see yourself.

what is 1/11 divided by 4?(FRACTION FORM)

Answers

Answer: 1/44

Step-by-step explanation:

question 9 i mark as brainliest ​

Answers

Answer:

I think the third one I'm not sure tho

Answer:95,826

Step-by-step explanation:

Please help me answer this :)?

Answers

Can you add an image please?

The two triangles below are similar. Which pair are corresponding sides?

LN and MN
MN and QR
LM and QR
LM and PQ
hola estas ahi​

Answers

MN and QR

Hope it helps...

A submarine dives 20 meters each minute for 15 minutes. What is the total change in depth after 15 minutes?

Answers

The correct answer is 300 meters

Answer:

300m

Step-by-step explanation:

20 Times 15=300

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