Answers
The vertex is located at (h,k)
The two roots p and q can be defined as such
p = h-rq = h+rwhere r is the horizontal distance between the vertex and either root. We use the same r value for each equation because of symmetry. The diagram below shows what I mean.
Let's add up those two equations to get
p+q = 2h
The left hand sides p and q add to p+q. The right hand sides add to (h-r)+(h+r) = 2h. Note the r's cancel.
From here, we divide both sides by 2 and we end up with
h = (p+q)/2
In short, if we know the roots p and q, then we find the x coordinate of the vertex (h) to be the average of those roots. You add up the roots and then divide by 2.
After you figure out the value of h, finding the value of k will have us plug in this h value into the quadratic equation and simplifying.
------------------------
Example:
Let's say we have the quadratic y = x^2 - 8x + 12. This factors to (x-2)(x-6)
Solving (x-2)(x-6) = 0 shows that x-2 = 0 becomes x = 2 and x-6=0 becomes x = 6.
So the roots here are p = 2 and q = 6. The order of the roots doesn't matter.
Averaging these roots gives us
h = (p+q)/2
h = (2+6)/2
h = 8/2
h = 4
The x coordinate of the vertex is x = 4.
Plug this back into the original equation to find...
y = x^2 - 8x + 12
y = (4)^2 - 8(4) + 12
y = 16 - 32 + 12
y = -16 + 12
y = -4
Or you could say
y = x^2 - 8x + 12
y = (x-2)(x-6)
y = (4-2)*(4-6)
y = (2)*(-2)
y = -4
Either way, we find that k = -4 is the y coordinate of the vertex
The vertex for this example is located at (h,k) = (4, -4)
Refer to the diagram below.
Related Questions
I’m having trouble trying to answer this question what is 68×70 this app it helps you work it gives you answers it’s not a cheating thing I should have said that
Answers
Answer:
4760.
Step-by-step explanation:
68 x 10: 680
680 x 7: 4760
Answer:
4760
Step-by-step explanation:
PLS HELP ASAP Ms. Farrell has 36 students in her class. This is 5 more
students than Mr. Carter has.
How many students does Mr. Carter have? Choose the correct equation and
answer.
A. X+36 = 5
x = 41 students
B. x+ 5 = 36
x= 41 students
O C. X+41 = 36
x= 77 students
D. x+ 5 = 36
x= 31 students
Answers
Answer:
its d 31 is 5 less than 36.....
A strawberry farmer will receive 37 per bushel of strawberries during the first week of harvesting each week after that the value will drop 0.8 per bushel the farmer estimates that there are approxiamately 129 of strawberries int he fieldsand that the crop is increasing at a rate of four bushels per week when should the farmer harvest the strawberries to maximize their value? (Assume that "during the first week of harvesting" here means week 1. How many bushels of strawberries will yield the maximum value? (Round your answer to the nearest integer.)
bushels
2. What is the maximum value of the strawberries? (Round your answer to two decimal places.)
$
Answers
Answer:
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
b.)
Revenue = bx = (157)(31.4) = $ 4929.8
Step-by-step explanation:
Let number of bushes = b
The price of the bushes = x
The time to harvest = t
The revenue = y
Now given,
Price = x = 37 - (0.8)t
and
Number of bushes = b = 129 + 4t
Also,
The revenue = (Number of bushes)(Price of the bushes)
= bx
= (129 + 4t)[37 - (0.8)t]
= 129×37 - 129× (0.8)t + 4×37t - 4×0.8t²
= 4773 - 103.2t + 148t - 3.2t²
= 4773 + 44.8t - 3.2t²
⇒ y = 4773 + 44.8t - 3.2t²
Now,
[tex]\frac{dy}{dt}[/tex] = 0 + 44.8 - 6.4t
Now,
[tex]\frac{dy}{dt}[/tex] = 0
⇒ 44.8 - 6.4t = 0
⇒ - 6.4t = -44.8
⇒ 6.4t = 44.8
⇒t = [tex]\frac{44.8}{6.4} = 7[/tex]
Now,
[tex]\frac{d^{2}y }{dt^{2} }[/tex] = -6.4
As [tex]\frac{d^{2}y }{dt^{2} }[/tex] < 0 ,
It means at time t = 7 , the revenue is maximum
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
Price = x = 37 - (0.8)(7) = 37 - 5.6 = 31.4
b.)
Revenue = bx = (157)(31.4) = 4929.8
PLS HELP
What is the length, in feet, of AD in the isosceles trapezoid ABCD?
15 ft
c
1410
5 ft
A
D
F
Note: Figure is not drawn to scale.
O 3 feet
O 10 feet
O 141 feet
O 21 feet
Answers
Answer:
21 feet
Explanation:
Using pythagorean theorem to find the length of the added length of the bottom.
A^2+B^2=C^2 or 4^2+B^2=5^2 or 16+B^2=25
25-16=9 so B^2 is 9 and the square root of that is 3 so B is 3. Then you add 15+3+3 to get 21.
Four friends are sharing 6 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
write what mixed number you got
Answers
Answer:
1 1/2 cups
Step-by-step explanation:
What is the value of the digit 9 in 71.92
Answers
Answer:
.90
Step-by-step explanation:
?
Is 2/6 greater than 1/2
Answers
Answer:
1/2 is greater hope it helps
Sal wrote the statement below to represent the inequality 8 n minus 5 less-than 25. Which words should Sal use to complete the verbal statement?
The product of 8 and n decreased by 5 is _________________ 25.
less than
greater than
less than or equal to
greater than or equal to
Answers
Answer:
greater than or equal to
Answer:
the above answer is correct, it is greater than or equal to
Step-by-step explanation:
Ples help me
IF its wrong i will report u
ill give you the best if it right and who ever is first.
Answers
Answer:
A, B, and D are equal to 75%
Step-by-step explanation:
Hope it helps!
Answer:
B., A. and D.
Because they all equal 75%!
Ralph Chase plans to sell a piece of property for $150000. He wants the money to be paid off in two ways a - short-term note at 11% interest and a long-term note at 8% interest. Find the amount of each note if the total annual interest paid is $15200
.
Answers
Answer:
Amount on 11% note = $106,666.67
Amount on 8% note = $43,333.33
Step-by-step explanation:
Let the amount for the short-term note at 11% interest be x.
Thus, the amount for the short-term note at 8% interest will be (150000 - x)
Now we are told that the total interest paid is $15,200.
Thus;
0.11x + 0.08(150000 - x) = 15200
0.11x + 12000 - 0.08x = 15200
Rearranging gives;
0.03x = 15200 - 12000
0.03x = 3200
x = 3200/0.03
x = $106666.67
Thus, amount for 8% note = $150000 - $106666.67 = $43,333.33
Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† If you want to provide your child with 340 calories and 75 grams of carbohydrates, how many servings of each should you use?
Answers
Answer:
2 servings of Gerber Mixed Cereal for Baby and 3 servings of Gerber Mango Tropical Fruit Dessert should be used.
Step-by-step explanation:
Given that Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates, while Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates, and you want to provide your child with 340 calories and 75 grams of carbohydrates, in order to how many servings of each you should use, the following calculation has to be made:
(80 x 5) + (60 x 0) --- (21 x 5) + (11 x 0) = 400 --- 105
(80 x 4) + (60 x 1) --- (21 x 4) + (11 x 1) = 380 --- 95
(80 x 3) + (60 x 2) --- (21 x 3) + (11 x 2) = 360 --- 85
(80 x 2) + (60 x 3) --- (21 x 2) + (11 x 3) = 340 --- 75
Therefore, 2 servings of Gerber Mixed Cereal for Baby and 3 servings of Gerber Mango Tropical Fruit Dessert should be used.
Elijah invested $280 in an account paying an interest rate of 2.1% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $360?
Answers
Answer: 12
Step-by-step explanation:
10
12
15
18
Are my choices
Answers
Answer:
y=10 x=30
Step-by-step explanation:
3x=90
x=30
2(30)+3y=90
60+3y=90
3y=30
y=10
Answer:
y= 10
Step-by-step explanation:
we have to find x first
∠ABD= 90° because its a right angle
3x°=90°
divide by on both sides
x= 30°
∠CBD must equal 90° degrees as well because a line is 180°
60+3y= 90
-60
3y=30
/3
y= 10
SOMEONE JUSt please HELP ME HELP ME PLEASE ITS URGENT
Answers
Answer:pretty sure it’s both 35°
Step-by-step explanation:
)) How many solutions does this equation have?
12 + 4t - 14t = -13t - 18
Answers
Answer:
t = -10
Step-by-step explanation:
Ok so,
12 - 10t = -13t -18
12 - 10t + 13t = -13t + 13t - 18
12 + 3t = -18
12 - 12 + 3t = -18 - 12
3t = -30
t = -10
hope this helps! have a good day!
Elena mixes 5 cups of apple juice with with 2 cups of ginger ale to make punch for a party she wants to make 35 cups of punch how much apple juice does she need to buy?
Answers
Answer:
25 cups of apple juice and 10 cups of sparking water.
Step-by-step explanation:
y=3x/5-6 in standard form
Answers
Answer:
The standard form is 3x-5y-30=0
(3x/5) - y = 6
3x - 5y = 30
Formula for parallelogram law of addition
Answers
Answer:
answers?
Step-by-step explanation:
Yin min owns A small store the first month store was open she made 1375 in profit during the next month she advertising local newspaper and saw a 60% increase in profit how much profit did she make the second month?
Answers
Hey there! As far as I understand the problem, she made $2,200 in profit. Take 1,375 and multiply it by 1.6.
Classify each number according to its value
5.2×10-4
Answers
Answer:
48
Step-by-step explanation:
first put 5.2 x 10 in parentheses . Which you do first then subtract 4 and you will get your answer.
Your supposed to do each half separately and the multiple them to together
Caroline borrowed 300,000 from the bank in order to buy a house. If the simple interest RATE that the bank charged her was 3.5%, and she ended up paying the bank back a total of $615,000 (principal and interest total), how long (in years) did it take her to pay back the loan?
Answers
Answer:
915'000.+123=915,123
I NEED HELP
Suppose 24 is 2%. What is 100%?*
Answers
Answer:
1200
Step-by-step explanation:
If 24 is 2%, 100% would be 1200 because if you multiply 2 by 50 you get 100% so you multiply 24 by 50 which is 1200
Answer:
20.
Step-by-step explanation:
The strategy here is to see how many times the "percent number" (in this case, 25) goes into 100, and then count by that number until we reach 100-the whole thing. Here, we're told that 25% of a number is 5. So, to find 100% of the number, we count by 25s up to 100: 25, 50, 75, 100. 100% is 20.
Graph the system below and write its solution.
-2x+y=-4
y=1/2x+2
Answers
Answer:
(4, 4)
General Formulas and Concepts:
Algebra I
Reading a Cartesian planeCoordinates (x, y)Graphing functionsSolving systems of equations by graphingStep-by-step explanation:
Where the 2 graphs intersect would be the solution set to the systems of equations.
Answer:
x=4
and
y=4
Step-by-step explanation:
let -2x+y=-4 ...1
y=1/2x+2 ...2
putting equation 2 in equation 1 we get,
-2x+(1/2x+2)=-4
opening the brackets we get,
-2x+1/2x+2=-4
(-4x+x)/2=-4-2
-3x/2=-6
-3x=-6×2
-3x=-12
x=-12/-3
x=4
putting value of x in equation 2
y=1/2(4)+2
y=2+2
y=4
hence, x=4 and y=4
Write an expression that is equivalent to 27e+24
ANSWER FOR 40 POINTS
Answers
Step-by-step explanation:
3(9e+8) is the correct answer of this qn
Hope this helps
Have a great day/night
(SAT PREP) FIND THE VALUE OF X PLEASE ASAP AWARDING BRAINLIEST!!
Answers
Answer:
116
Step-by-step explanation:
x=180-(25+39+15)=116degrees
Answer:
116 is the correct answer to this question
anyone know which company charges the greatest rate per window?
Answers
Company B costs most per window
Step by step:
company a = 25x + 50
company b = 40x + 15
company c = 35x + 25
Rudy correctly solved the equation 10 = 4r.
Which statement describes his solution?
A
The solution is 40 since 10 times 4 equals 40.
The solution is 2.5 since 4 times 2.5 equals 10.
С
The solution is 2.5 since 4 divided by 2.5 equals 10.
D
There is no solution because no value can be multiplied by 4 to get 10.
Answers
Answer:
its B
Step-by-step explanation:
a) Work out
16.3-4.97 + 8.6
(2)
I
b) Work out
2164.89 +7
(2)
Answers
Answer:
a)19.93 b)2171.89
Step-by-step explanation:
a) As there are no brackets first do the equation
16.3-4.97 which is 11.33
then you add 8.6 onto that which is 19.93
b)2.164.89+7=2171.89
Jason planted 11 packs of seed in his 4 gardens. he Planted the same amount of seed in each garden. how many packs of Seed Were planted in each were planted in each garden?
Answers
2.75 packs
Step-by-step explanation:
11 packs ÷4 gardens =2.75 packs per garden
There are 18 black and 12 navy socks in your drawer. The room is dark and you
cannot turn on the light. What is the least number of socks that you have to take out of
your drawer to be certain that you have a pair of black socks?
Answers
The least number of socks that you have to take out of the drawer to be certain that you have a pair of the same color is 5 and the color is black.
Given that,
There are 18 black socks and 12 Navy socks in your drawer the room is dark and you cannot turn on the light.
We have to determine
What is the least number of socks that you have to take out of your drawer to be certain that you have a pair of black socks?
According to the question,
The following steps can be used in order to determine the least number of socks that you have to take out of the drawer:
The total number of blue socks is 18,
And the total number of navy socks is 12.
The probability that the socks come out is black socks is,
[tex]\rm P_b = \dfrac{18}{18+12}\\\\P_b= \dfrac{18}{30}\\\\P_b = \dfrac{3}{5}[/tex]
And the probability that the socks come out is navy socks is,
[tex]\rm P_n = \dfrac{12}{18+12}\\\\P_n= \dfrac{12}{30}\\\\P_n = \dfrac{2}{5}[/tex]
On comparing both the probability,
[tex]\rm P_b>P_n[/tex]
Hence, The least number of socks that you have to take out of the drawer to be certain that you have a pair of the same color is 5 and the color is black.
For more details refer to the link given below.
https://brainly.com/question/19200823
Answer:3
Step-by-step explanation:
I found this out because is you take 3 out you will get BLUE BLUE BLACK or BLACK BLACK BLUE or BLUE BLUE BLUE or BLACK BLACK BLACK
Hope that helps