Determine the (x, y) coordinates of the vertex of the parabola that represents each of the following functions:
Answers
The vertices of the parabolae are:
(h, k) = (- 3, - 1)(h, k) = (1, - 9)(h, k) = (4, 1)(h, k) = (3/4, 9/4)(h, k) = (- 3, 2)(h, k) = (0, 36)(h, k) = (7/2, 9/4)(h, k) = (5, - 1)(h, k) = (1, - 3)(h, k) = (- 1/2, 1)How to find the coordinates of the vertex of a parabola
Parabolae are represented by quadratic equations. In this problem we have parabolae in standard form and we need to determine its vertex form to find the needed information. Now we summarize the forms of quadratic equations:
Standard form
y = a · x² + b · x + c (1)
Vertex form
y - k = C · (x - h)² (2)
Please notice that (x, y) = (h, k) represents the vertex of the parabola.
To change quadratic equations from standard form into vertex form we need to apply algebraic handling:
y = x² + 6 · x + 8
y + 1 = x² + 6 · x + 9
y + 1 = (x + 3)²
(h, k) = (- 3, - 1)
y = x² - 2 · x - 8
y + 9 = x² - 2 · x + 1
y + 9 = (x - 1)²
(h, k) = (1, - 9)
y = - x² + 8 · x - 15
y = - 1 · (x² - 8 · x + 15)
y - 1 = - 1 · (x² - 8 · x + 16)
y - 1 = - 1 · (x - 4)²
(h, k) = (4, 1)
y = - 4 · x² + 6 · x
y = - 4 · [x² - (3/2) · x]
y + (- 4) · (9/16) = - 4 · [x² - (3/2) · x + 9/16]
y - 9/4 = - 4 · (x - 3/4)²
(h, k) = (3/4, 9/4)
y = x² + 6 · x + 11
y - 2 = x² + 6 · x + 9
y - 2 = (x + 3)²
(h, k) = (- 3, 2)
y = - x² + 36
y - 36 = - x²
(h, k) = (0, 36)
y = - x² + 7 · x - 10
y = - (x² - 7 · x + 10)
y + (- 1) · (9/4) = - (x² - 7 · x + 49/4)
y - 9/4 = - (x - 7/2)²
(h, k) = (7/2, 9/4)
y = x² - 10 · x + 24
y + 1 = x² - 10 · x + 25
y + 1 = (x - 5)²
(h, k) = (5, - 1)
y = 2 · x² - 4 · x - 1
y = 2 · (x² - 2 · x - 1/2)
y + 2 · (3/2) = 2 · (x² - 2 · x + 1)
y + 3 = 2 · (x - 1)²
(h, k) = (1, - 3)
y = - 4 · x² - 2 · x
y = - 4 · [x² + (1/2) · x]
y + (- 4) · (1/4) = - 4 · [x² + (1/2) · x + 1/4]
y - 1 = - 4 · (x + 1/2)²
(h, k) = (- 1/2, 1)
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Related Questions
What is the unit ratio for 360 oranges growing to 9 trees
Answers
Answer:
360/9=40
Step-by-step explanation:
Answer:
40
all you have to do is divide the first term by the second term
example: 360 divided by 9 = 40
Evaluate each expression when y=5.
B. 4(y+3)
Answers
Answer:
B. 4(y+3)=4(5+3)=4×8=32
Answer:
32
Step-by-step explanation:
Step 1: Sub y = 5 into the expression
Find anywhere that has a 'y' and replace it with a 5
4(y+3)
4(5+3)
Step 2: Solve
Use BEDMAS to solve the expression
4(5 + 3)
4(8)
32
Step 3: Therefore Statement
Therefore the expression is equal to 32
Simplify
(2a²b)(4ab)
Answers
Answer:
8a^3b^2
Step-by-step explanation:
Find the rule. Solve for n.
Answers
Answer:
X is always 1+ bigger than Y
EX: if you have y as 9, X will be 10
Step-by-step explanation:
N = 9
P = R+C help I need to get out of class plz help
Answers
Answer:
People's Republic of China
PRC means People's Republic of China.
Step-by-step explanation:
What is PRC? History of rebranding
All products manufactured in China were automatically considered low-quality items for a long period. Even the famous brand or name of the manufacturing plant did not manage to change this stereotype.
China has been the world leader in exporting and manufacturing industrial output since 2014. For the last 50 years, over 370 thousand new factories have started working in the PRC. To reduce the prime cost of goods, a lot of factories have been moved from Europe to China. The remaining factories, for example, those in Germany, France, and Spain, make products for their home markets but produce all goods for export in China.
When you are choosing household appliances pay attention to labels. You will find that most products of highly popular brands are marked “Made in China”. However, it doesn’t mean that – say – a kitchen unit is an imitation of a real food processor from Moulinex, for instance. The fact is that this unit was made at the Moulinex factory in China and it was then sent to your country. The real cost of the food processor produced in China is several times lower than the same one manufactured in and delivered from France. When ordering goods to be produced in China the seller earns more than when producing a similar product in France. Therefore there are so many European brands in our stores, which were produced in China.
European brands produced in China
Spare parts for smartphones from China
The case of spare parts for smartphones, tablets and laptops is even more complicated. It is commonly known that almost all spare parts are produced in China. Nevertheless, to buy a spare part for Samsung or Apple here is almost impossible. Their factories are protected by all means available. Spare parts from these factories are sent to Europe, where they are distributed among branches. Therefore you can buy the Original item only in the company's official representative office.
However, the Chinese people would not be Chinese if they were not able to make money on such expensive products. They manufacture the same spare parts but not at official factories. After learning the manufacturing technology of displays, touchscreens and flat cables, the local craftsmen create a device that can make spares identical to the original. Such spare parts are considered high quality products and belong to the High Copy level.
Original PRC means that the spare part consists of original components. For example, the seller has original LCDs and doesn’t have original touchscreens. In such cases, the High Copy touchscreen is installed on the original display. Such LCD module will be classified as Original PRC because one of its components is original. There can also be another scenario. Imagine that the seller has both the original LCD and touchscreen but the customer needs a module, not a separate spare part. In this situation, a handyman sticks together the LCD and the touchscreen and here is the module. Such a spare part is called Original PRC because it’s made of original components even though it is not manufactured at the official factory. The main difference between Original PRC and Original is the place where they were made. The quality of Original PRC spares doesn’t differ from Original. Still the difference in price is significant.
(hope this helps can i plz have brainlist :D hehe)
It says 33cm it’s messed up because it’s on a laptop but what’s the volume of this sphere :)
Answers
Answer:
1.51*10^5 cm^3
Step-by-step explanation:
the formula for the volume of a sphere is (4/3)pi(radius)^3
I can't really tell if the 33 cm is for the radius or the diameter, but it looks like the radius, so
(4/3)*(33)^3*pi
simplify
Im assuming you can use a calculator because it's too hard to do without because it's a huge number
help please will give brainliess
Answers
Card 1= 20
Card 2= nOt sure
Card 3=28
Card 4= 40
Hope this helps!
Isabel put $4,000 into a saving account that pays interest monthly at a simple-interest rate of 2.5% per year. If she takes the interest interest out of the account each month, how much money should she expect to earn after 6 months?
Answers
9514 1404 393
Answer:
$49.98
Step-by-step explanation:
The interest credited to Isabel's account each month is ...
I = Prt
I = $4000·(0.025)(1/12) = $8.33
If she withdraws that amount each month, the original balance is restored, and she will earn the same amount the next month.
Isabel's total earnings in 6 months will be ...
$8.33 · 6 = $49.98
Part B: The weatherman claimed that the temperature on Friday was the opposite of Thursday’s temperature. Which of the following statements support this claim? Select all that apply.
A.
The temperatures on Thursday and Friday are opposites because they are on different sides of 0 on the number line.
B.
The temperatures on Thursday and Friday are opposites because they have a sum of 0.
C.
The temperatures on Thursday and Friday are opposites because they both contain a 3.
D.
The temperatures on Thursday and Friday are opposites because they are the same distance from 0 on the number line.
Answers
Answer:
it will be d
Step-by-step explanation:
because I had a assignment over this and I put d and got it correct
pls answer this question
Answers
Answer:
id kkk what the quequestion is
Step-by-step explanation:
urgent urgent urgent plz
Answers
what does 19+r=
PLEASE HELP
Answers
Solve the given equation
7/10X=4 3/5
Answers
Answer:
x
=
40
Step-by-step explanation:
Solve using elimination
x+y=7
x-y=-3
Answers
Answer:
I think it's 4
Step-by-step explanation:
if x+y is 7 and x-y is 3 then the answer is 4
Answer:
X=2, y=5
Step-by-step explanation:
X+y=7
x-Y=-3
————-
2x+ 0 =4
2x=4
x=2
solve for y using either equation
x+y=7
2+y=7
y=5
check answers by substituting x and y value in either equation:
x+y=7
2+5=7
7=7
or
x-y=-3
2-5=-3
-3=-3
What is the relationship between the angle of depression of a person looking down from the top of a hill at their friend standing on the ground and the angle of elevation of the person on the ground looking up at their friend who is standing on top of the hill?
a. the angle of elevation will be greater than the angle of depression because the person has to look up from the ground to see their friend at the top of the hill
b. The angle of depression and angle of elevation will add to 180°
c. The angle of depression and angle of elevation will be the same
d.The angle of depression would be greater than the angle of elevation because the hill is higher than the ground
Answers
Answer:
C) angle of depression and angle of elevation will be the same.
this is because the horizontal for angle of elevation and angle of depression are parallel
therefore, the two angles are same (alternate angles)
hope it helps.
pls mark brainliest !!!
The correct answer is (c) The angle of depression and angle of elevation will be the same.
What is an angle of depression?When a person is standing on top of a hill and looking down at their friend standing on the ground, the angle formed between the line of sight and a horizontal line is called the angle of depression.
Similarly, when a person on the ground is looking up at their friend who is standing on top of the hill, the angle formed between the line of sight and a horizontal line is called the angle of elevation.
Since the two angles are formed by the same two points and are measured with respect to the same horizontal line, they will be congruent or the same. Therefore, option (c) is correct.
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The highest point in Chicago is 735 feet above sea level. You can represent that numerically using .
Answers
Answer:
+735 feets
Step-by-step explanation:
Points or position above sea level are denoted with positive elevation values while points or positions below sea level are denoted by negative values. The sea level position itself could be viewed as a midpoint such as the position of 0 on a number line ; where distances to the right are positive and distances to the left are negative.
Hence, a point which is said to be 735 feets above sea level would have an equivalent numeric representation of +735 feets
Which of the following points fall above the line y = x ??
a) (2, 2)
b) (-4,-5)
c) (3, -3)
d) (6,4)
e) (0,9)
Answers
Answer:
a) (2,2)
Step-by-step explanation:
as X=2 and y=2
y=x
If line a and line b are parallel, which angles are same-side Interior angles?
A.23 and 211
B. 28 and 23
C. 27 and 23
D. none of these
Answers
Answer:
i think its C. 27 tp 23 ****PLEASE HELP ME ANYONE
Answers
i believe it’s (0,4) since it’s asking for vertex.
how do you solve 3 divided by x -1 = x + 1
Answers
Answer:
multiply (x-1) to both sides and then subtract three from both sides
3 = (x-1)(x+1)
3 = (x^2 -1)
0 = x^2 - 4
(x-2)(x+2) = 0
x = 2
x = -2
Step-by-step explanation:
what is the distance between (-1,-2) and (8,10)
Answers
Answer:
x1 = 2, x2 =-8
y1=-2, y2 =-2
y2-y1 = |-2+2| =0
x2-x1= |-8-2|= 10
So distance is 10 units
Step-by-step explanation:
-3 + 4g = 7g. Solve for g.
Answers
Answer:
g=-1
Step-by-step explanation:
-3 + 4g= 7g
-4g. -4g
g=-1
Solve for N.
N - 26 = 72
N - 26 +
= 72 +
N =
Answers
Answer:
98
Step-by-step explanation:
Solve : n-98 = 0
Add 98 to both sides of the equation :
n = 98
Find the value of X:
Answers
Answer:
x=9
Step-by-step explanation:
I took one side, and made proportions:
12:16
3:4
so, x-1:6=3:4
(x-1)/6=3/4
solve it for x=9
Answer:
9
Step-by-step explanation:
Hope this helps!
Plz Mark Brainliest!
beş üzeri üç ekşi otuz bölübeş eksi iki üzeri iki işlemini sonucu aşağıdakilerden hangisidir?
A) 15
B) 78
C) 95
D) 115
cevaplarınızı bekliyorum.
Answers
Ce clasă ești sa văd daca te pot ajuta
If Ms. Wong takes out a loan of 85000 dollars with a simple interest of 5% annually, how much would she have to pay in 2 years if she returns 35000 after the first year? Show your work and your thinking.
(PLEASE HELP !!)
Answers
Answer = 6,760 in interest + the original 85,000 = 91,750
What is the solution of 2.5z = 27.5
Answers
Let's solve your equation step-by-step.
2.5z=27.5
Step 1: Divide both sides by 2.5.
2.5z/ 2.5 = 27.5/ 2.5
z=11
Answer:
z=11
Find the midpoint of the interval [-3, 6] along the number line.
Answers
Answer:
1.5 or 3/2
Step-by-step explanation:
The midpoint of the interval [-3, 6] along the number line is 1.5.
The midpoint of an interval is the point that lies exactly in the middle of the two endpoints.
To find the midpoint of the interval [-3, 6], we use the midpoint formula:
Midpoint = (Endpoint1 + Endpoint2) / 2
In this case, Endpoint1 is -3, and Endpoint2 is 6:
Midpoint = (-3 + 6) / 2
Midpoint = 3 / 2
Midpoint = 1.5
The midpoint of the interval [-3, 6] is 3/2. This means that the point exactly halfway between -3 and 6 on the number line is 1.5 units to the right of -3 and 1.5 units to the left of 6.
Visually, if you plot -3 and 6 on a number line, the midpoint 3/2 (or 1.5) would be located at the center, equidistant from both endpoints.
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Things that are equivalent to 5 : 2
Answers
Answer:
2/5
Step-by-step explanation:
Answer:
10 : 4, 15 : 6, 20 : 8,
Step-by-step explanation:
increase the first number by 5 then add two to the second number
simplify e with an exponent of in6
Answers
Answer:
Step-by-step explanation:
I think the exponent is ln6, not in6.
e^(ln 6)= 6