Answers
9514 1404 393
Answer:
a) y = (x -4)² -4
b) (4, -4)
c) translated 4 right, 4 down
Step-by-step explanation:
a) Apparently "graphing form" is a reference to "vertex form." That form is ...
y = a(x -h)² +k . . . . . . parabola with vertex (h, k) and vertical scale factor 'a'
The coefficient of x² in your given equation is 1, so a=1. The values of h and k can be found as follows.
'h' is the opposite of half the x-coefficient in your equation, so is h = -(-8/2) = 4. The value of k is the square of h, subtracted from the constant in your equation: k = 12 -h² = 12 -16 = -4. (This applies when a=1, as here.) These calculations are the "cut to the chase" version of "completing the square."
The method of "completing the square" has you consider the x-terms separately from the constant term:
y = (x² -8x) +12
To "complete the square", you want to make the terms in parentheses be a perfect square trinomial. You do that by adding the square of half the x-coefficient. In order to keep the same equation, you need to subtract an equivalent amount outside parentheses:
y = (x² -8x +(-8/2)²) +12 -(-8/2)² . . . . . add and subtract (-8/2)²
y = (x -4)² +(12 -16)
Then the vertex form is ...
y = (x -4)² -4 . . . . and the vertex is (h, k) = (4, -4).
The graphing calculator plot attached confirms this vertex value.
__
The problem statement tells you that you can also find this form by averaging the x-intercepts. If you factor your equation, you get ...
y = (x -6)(x -2)
The x-values that make these factors zero {6, 2} are the x-intercepts. Their average (6+2)/2 = 4 is the x-coordinate of the vertex (h). You can find the y-coordinate of the vertex by evaluating y when x=4: y = 4² -8·4 +12 = -4. So, the vertex by this method is (h, k) = (4, -4), and the equation in graphing form is ...
y = (x -4)² -4 . . . . as above.
__
b) As we saw above, the vertex coordinates are (h, k) = (4, -4).
__
c) The vertical scale factor 'a' is 1, so the only transformation done on the graph is to move the parent vertex (0, 0) to the location (4, -4). That is, the graph has been translated 4 units right and 4 units down. (In the attached, the parent function is shown with a dashed line.)
Related Questions
someone help please?
Answers
Use “3” as “r” in the formula.
5x^2-12=88 solve algebraically
Answers
Answer:
x = 2sqrt(5) or x = -2sqrt(5)
Step-by-step explanation:
5x^2 - 12 = 88
5x^2 = 100
x^2 = 20
x = +/- sqrt(20)
x = 2sqrt(5) or x = -2sqrt(5)
Answer:
[tex]x_1=-2\sqrt{5},\ x_2=2\sqrt{5}[/tex]
Step-by-step explanation:
Given equation: [tex]5x^2-12=88[/tex]
Step 1: Add 12 to both sides.
[tex]\\\implies 5x^2-12+12=88+12\\\\\implies 5x^2=100[/tex]
Step 2: Divide both sides by 5
[tex]\\\implies\dfrac{5x^2}{5}=\dfrac{100}{5}\\\\\implies x^2=20[/tex]
Step 3: Take the square root of both sides (positive and negative roots).
[tex]\\\implies \sqrt{x^2}=\sqrt{20}\\\\\implies x=\pm\ \sqrt{20}[/tex]
Step 4: Simplify.
[tex]\\\implies x=\pm\ \sqrt{4\times5}\\\\\implies x=\pm\ 2\sqrt{5}[/tex]
Step 5: Separate into two cases.
[tex]\implies x_1=-2\sqrt{5},\ x_2=2\sqrt{5}[/tex]
Another example:
https://brainly.com/question/20778317
How can you use the coordinates of two points on a line to determine the slope of the line?
Answers
Answer:
you can use the slope intercept formula!
y2-y1/x2-x1
Step-by-step explanation:
lets take an example!
the coordinates of 1 point are (2,4) and the other point is (4,6)
so lets plug in (x1,y1) (y1,y2)y2 is the y intercept of second point so it is 6 minus y1 which is 4.
6-4/x2-x1
lets do same for x!
6-4/4-2
lets solve
2/2
=1
the slope is 1
Wilson is 6 years older than Mary. Wilson's age is 10 years less than five times Mary's age. The equations below model the relationship between Wilson's age (w) and Mary's age (m):
w = m + 6
w = 5m − 10
Which is a possible correct method to find Wilson's and Mary's ages?
Solve w + 6 = 5w − 10 to find the value of w.
Write the points where the graphs of the equations intersect the x axis.
Solve m + 6 = 5m − 10 to find the value of m.
Write the points where the graphs of the equations intersect the y axis.
Answers
Answer:
no 4=f
Step-by-step explanation:
dwfn sdv and it appers to be marys age ;)
think before you do something rude
Answer:
C. Solve m + 6 = 5m - 10
Step-by-step explanation:
Wilson is 6 years older than Mary.
(MARY's age + 6 = WILSON's age)
Wilson's age is 10 years less than five times Mary's age.
(MARY's age * 5 - 10years = WILSON's age)
(Mary is 4 years old and Wilson is 10:
4 + 6 = 10
4(5) = 20 - 10 = 10
just in case you were curious)
Good luck!!
(2x^3+10x^2)/(x^2+x-20) divided by (2x^2)/(x-4)
Answers
Answer:
1
Step-by-step explanation:
Who knew the answer would be 1 LOL
hope this helps :)
The temperature was 80 °F and then fell 20 °F. What is the new temperature?
Answers
Hope this helps have a nice day :) !!!
Abdul can type 23 words per minute. Abdul has a 500-word essay to type for his English teacher. How long will it take him to type it? Round your answer to the nearest minute.
pleaseeee
Answers
Answer:
22 minutes. (rounded)
Step-by-step explanation:
Ok so what your going to do is just divde.
You divide and get 21.7
So round it and you will get 22 minutes.
If a radioactive substance is quickly decaying at a rate of 13% per hour approximately how much of a 200 pound sample remains after one day? *
A. 7.1
B. 2.3
C. 25.6
D. 15.6
Answers
Answer: 7.1
Step-by-step explanation:
Exponential functions: y=ab^x
A = starting value
R= rate ex: 3% = .03
B= 1 + r
Then write your exponential function
find the probability that a number chosen at random from the integers between 5 and 16 inclusive is a multiple of 3 or a mutiple of 2
Answers
Answer: Numbers between 5 and 16 are:-
6, 7, 8, 9, 10, 11, 12, 13, 14 , 15 and 16.
Therefore, total number of outcomes =11
Numbers inclusive between 5 and 16 which are divisible by 2 or 3 are-
6 , 8, 9 ,10 ,12, 14 and 15.
Number of favourable outcomes = 7
Therefore, probability of getting a number which is either a multiple of 2 or 3 is:
p(e) = \frac{7}{11}p(e)=
11
7
HENCE, THE REQUIRED PROBABILITY IS = 7 / 11.
Step-by-step explanation: does this help?
The population of a city increases by 2.7% per year. If this year's population is
197,000, what will next year's population be?
Answers
im not sure sorry
also make you 2021 be better than your 2020 and stay safe
MATH LOVERS!!! Can u send me a pic of you filling this out plz!!!!
Answers
Answers
Located In The Following Attachments
High Hopes
Barry-
Answer:
you would just do 2/3*-6-1= -5
and you would fill in the numbers in the x column and solve
5-1/2*-2=6
and you would replace x with the number in the x column
(ik i already helped you on this lol)
have a great day/night
In the picture I need the answers to the questions.
Answers
Answer:
a) [tex]\mathbf{ f(g(x))=x+2\sqrt{x} +1}[/tex]
b) [tex]\mathbf{f(g(9))=16}[/tex]
Step-by-step explanation:
We are given:
[tex]f(x)=(x-2)^2\\g(x)=\sqrt{x} +3[/tex]
We need to find [tex]a) f(g(x))\\b) f(g(9))[/tex]
a) First finding: [tex]f(g(x))[/tex]
It can be found by putting the value of g(x) into f(x)
We are given:
[tex]f(x)=(x-2)^2\\Put\:x=g(x)\:i.e. \: x= \sqrt{x} +3\\f(g(x))=(\sqrt{x} +3-2)^2\\Now\: solving:\\f(g(x))=(\sqrt{x} +1)^2\\Using\:formula\:\mathbf{(a+b)^2=a^2+2ab+b^2}\\f(g(x))=(\sqrt{x})^2+2(\sqrt{x} )(1)+(1)^2\\ f(g(x))=x+2\sqrt{x} +1[/tex]
SO, we get: [tex]\mathbf{ f(g(x))=x+2\sqrt{x} +1}[/tex]
b) Now finding: [tex]f(g(9))[/tex]
It can be found by putting x=9 in f(g(x))
We have:
[tex]f(g(x))=x+2\sqrt{x} +1\\Put\:x=9\\f(g(9))=9+2\sqrt{9}+1\\We\:know\: \sqrt{9}=3\\ f(g(9))=9+2(3)+1\\f(g(9))=9+6+1\\f(g(9))=16[/tex]
So, we get: [tex]\mathbf{f(g(9))=16}[/tex]
What is the amount of INTEREST paid on this loan: Principal: $3,500 Rate: 14% Term: 2 years
Answers
Answer:
Annual interest rate for this loan. Interest is calculated monthly on the current outstanding balance of your loan at 1/12 of the annual rate.
Monthly loan payment is $400.76 for 60 payments at 7.5%.
Step-by-step explanation:
Calculate:PaymentAmount
?Loan amount:*Enter an amount between $0 and $100,000,000
$20,000
?Monthly payment:
$401
?Interest rate:*Enter an amount between 0% and 25%
7.5%
?Term in months:*Enter an amount between 1 and 480
60
Total interest paid:$4,045.51
Total payments:$24,045.51
Describe the relationship between the two quantities. WILL GIVE BRAINLIEST NO JOKE ANSWERS PLEASE..
Answers
Answer:
Between the two quantities, the sales have a longer increase rate for dollars than the bicycle has for speed, and the bicycle travel had a good speed rate, but slowed down the increased again.
Step-by-step explanation:
What could it mean to say there is a 100% decrease
in a quantity? Give an example of a quantity where this
makes sense.
URGENT PLEASE!!!
Answers
ﾟ+*:ꔫ:*
A. (2, 1)
B. (1, -2)
C. (1, 2)
D. (-1, 2)
♡━━━━━━━━━♡
︎thank you! ♡´･ᴗ･`♡
Answers
Answer:2,1
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
HELP ASAP!!!!!!!
PLS I NEED THIS TURNED IN IN 10 MINS
Answers
Answer:
slope = 2
y-int = 3
Step-by-step explanation:
y-intercept can be determined by the coordinate (0,3) which is 3 units up from origin on the y-axis
slope can be determined by taking the difference of a pair of y-values and dividing it by the difference of the x-values
ex, 3 - 1 = 2
0 - (-1) 1
or: 5 - 3 = 2
1 - 0 1
Under her cell phone plan, Hannah pays a flat cost of $65.50 per month and $4 per
gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would
have to pay for 3 whole gigabytes.) She wants to keep her bill under $70 per month.
What is the maximum whole number of gigabytes of data she can use while staying
within her budget?
Answers
Answer:
1 gigabyte
Step-by-step explanation:
70-65.50=4.5
The maximum whole number of gigabytes of data she can use while staying within her budget 2 gigabytes.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now given that,
Flat cost per month = $65.50
Cost per gigabyte = $4
Let x be the total gigabytes she uses in a month.
Thus, Cost of gigabytes of month = 4x
So, total bill of the month = 65.50 + 4x
Now since, Hannah wants to keep her bill under $70 per month
⇒ 65.50 + 4x ≤ 70
Subtracting 65.50 both the side we get,
4x ≤ 70 - 65.50
⇒ 4x ≤ 4.50
Dividing 4 both the side we get,
⇒ x ≤ 1.125
Since she has to pay for the whole gigabytes
⇒ x ≤ 2
which is the required gigabytes she can use to keep her bill $70.
Thus, the maximum whole number of gigabytes of data she can use while staying within her budget is 2 gigabytes.
To learn more about inequality :
https://brainly.com/question/13363104
#SPJ2
Carlos needs to save an additional $565 before he can purchase a car for his son he plans to save $25 each week at this rate at the end of how many full weeks will he have enough money to purchase the car
Answers
Given:
Savings for each week = $25
Amount required before Carlos purchase a car = $565
To find:
The number of full weeks in which he will have enough money to purchase the car.
Solution:
Let the required number of weeks be x.
Savings for 1 week = $25
Savings for x week = $25x
Savings must be greater than equal to $565 to purchase the car.
[tex]25x\geq 565[/tex]
Divide both sides by 25.
[tex]x\geq \dfrac{565}{25}[/tex]
[tex]x\geq 22.6[/tex]
So, the smallest possible integer value of x is 23.
Therefore, 23 week are required to have enough money to purchase the car.
Which property is illustrated? 8(a + c) = 8a+ 8c
Answers
Answer:
Distributive property
Step-by-step explanation:
Here, we want to evaluate the property illustrated
From what we can see, we have that each of the inner values are multiplied by the outside value
This is simply a display of distributivity
We can conclude that we have a right distributive property in place here
What is this question?
Answers
Answer:
A
Step-by-step explanation:
So timing a fraction with a fraction smaller by 1 means its a proper fraction.
And it can't get bigger than it already is because it's timing a less than 1 itself.
So it's A, it will be smaller
evaluate _1001 3.
please guys this one answer me
please follow me
Answers
Answer:
here is your answer....
(1001)^3
(1000+1)^3
1000^3+3*1000^2*1+3*1000*1^2+1^3
1000000000+3*1000000+3*1000+1
1000000000+3000000+3000+1
ans: 1003003001 ..
I hope this will help you...
the number of members in 20 families in a village is given as 6,8,6,3,2,5,7,8,6,5,5,7,7,8,6,6,7,7,6,5
how many families have more than 5 members
step by step explanation please answer this... don't spam
Answers
Answer:
2
6,6,6,6,6,6=more than 5
7,7,7,7,7=has exactly 5 members
Steve decreased the number of miles he ran from 25 to 18. By what percent did the number of miles decrease?
Answers
Answer:
28%
Step-by-step explanation:
1) 25-18=7(your decreased value)
2) 7(decreased value of miles ran)/25(overall number of miles ran)
3) 7/25*4/4 (this will make the denominator 100)=28/100=28%
What is the value of x?
(2x + 15)°
to
2x
A. 24
B. 33
C. 72
D. 75
Answers
Answer:
D. 75
Step-by-step explanation:
Simplify the following by combining like terms: 10 + 7r+b-4r*
10+ 3r
O 10 + 3r + b
O 13r + b
Answers
Explanation trust in de way
Algebra 1 Honors
BUSINESS a printing press valued at $120,000depreciates 12% per year. What will be the approximate value for the printing press in 7 years?
A. $19,200 B. $265,282 C. $49,041 D. $55,728
Answers
Answer:
19200
brainliest if correct
Explanation
12% of 120,000 = 14400
14400x7 = 100800
120,000 - 100800 = 19200
Factor the expression completely. 10x^5 -7×^3?
Answers
Answer:
there is your answer hope that helps
all the multiples of 5 are multiples of 10
Answers
Answer:
False
Step-by-step explanation:
This is the answer because:
1) All the multiples of 5 are not multiples of 10 because multiples of 10 end in zeros and not all the multiples of 5 end in a zero.
Therefore, the answer is false.
Hope this helps! :D
Answer: false
Step-by-step explanation: say for instance 25 (5•5) is not a multiple of 10
Why does the narrator state that taking the road less traveled has made all the difference?
Answers
Answer:
See below
Step-by-step explanation:
The phrase itself is a famous few lines extracted from "The Road Not Taken" by poet Robert Frost. The statement "taking the road less traveled" means that someone is acting independently, freeing themselves from the conformity of others (who choose to take 'the road more often traveled.'), generally making their own choices, and perhaps leaving a new trail that will become the road more often traveled