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
The perimeter of a dance floor is 44 feet.
The length is 8 feet less than twice the width.
Let I=length and w=width.
0 21 + 2w = 44
1 = 2w - 8
21 + 2w = 44
w= 21 – 8
0 21 + 2w = 8
1 = 2w - 44
O 1 + w = 44
1 = 2w – 8
Answers
Answer:
Step-by-step explanation:
Not sure what the question is here.
L = W-8
Perimeter = 2L + 2W = 44
L+W = 22
(W-8)+ W = 22
W = 15 ft
L = 7 ft
Is 3 1/2 cups more or less than 1 liter? Explain your reasoning. (Note: 1 cup ≈ 236.6 milliliters)
Answers
Answer:
no you need about 4.2 cups for a liter
Step-by-step explanation:
olivia's passcode has 4 digit The second digit to the left is 3 times the first (left most) digit tHe number formed by the last (right most ) 2 digits is three times the second digit to the left.the sum of the digits is 21. what is olivia's pass code
Answers
Answer:
3927
Step-by-step explanation:
This is the answer my teacher gave me, I promise.
The four-digit passcode is 3927 and this can be determined by using the given data and by using the hit and trial method.
Given :
Olivia's passcode has 4 digits. The second digit to the left is 3 times the first (left most) digit.The number formed by the last (right most) 2 digits is three times the second digit to the left.The sum of the digits is 21.Let the four digits passcode be 'abcd'. Then mathematical expression that represents "The second digit to the left is 3 times the first (left most) digit" is given below:
b = 3a --- (1)
The mathematical expression that represents "the sum of the digits is 21" is given below:
a + b + c + d = 21 --- (2)
So, let a = 3, then b = 9, and the last two digits are 27. So, the number becomes 3927.
For more information, refer to the link given below:
https://brainly.com/question/25277954
1/1-cos x
+
1/1+cos x
Answers
Answer:
2 csc^2 x
Step-by-step explanation:
using a common denominator, that is
((1+cosx)+(1-cosx))/(1-cos^2c) = 2/sin^2x
Answer:
sin^2x
Step-by-step explanation:
(1+cosx)(1-cosx)
Difference of squares
1-cos^x
Pythagorean identity
sin^2x
Consider the system of linear equations shown here. x – 4y = -8 y = -X – 3 What is the solution to this system? How do you know?
Answers
Answer:
x = -4
y = 1
Step-by-step explanation:
For the "How do you know?" part, substitute the x and y values into one the original equations and check to see if it's true
Latoya opened a savings account and made an initial deposit. After the initial deposit,she added money into the account each week. She added the same amount of money each week, and she did not make any withdrawals. After 4 weeks, she had $450 in her account. After 9 weeks, she had $825 in her account. How much money is Latoya adding to her account each week?
Answers
Answer:
Apologies, but you need to tell me the initial deposit amount in order to solve this.
Step-by-step explanation:
;-; mark brainliest to make you feel better
Answer:$50
Step-by-step explanation:
What is the Unknown number in proportion
Answers
Answer:
8*7/4=7x
56/4=7x
14=7x
x=2
Step-by-step explanation:
3.
a) Find the HCF of 45 and 60
b) Find the LCM of 45 and 60
c) Multiply your answers to parts a and b together.
d) Multiply 45 and 60.
Answers
Answer:
a- 15
Step-by-step explanation:
Answer:
a.) 15
b.) 180
c.) 2700
d.) 2700
10° 70° 110° 170° are my choices
Answers
Answer: 70 sorry if wrong
Step-by-step explanation:
Answer:
70°
Step-by-step explanation:
Hi!
So, according to the verticle angle theorem:
[tex]2x+50=7x[/tex]
Now just solve this equation
Same to both sides:
[tex]50=5x[/tex]
[tex]x=10[/tex]
Plug in numbers to 2x+50
[tex]2(10)+50[/tex]
[tex]20+50\\70[/tex]
Is x^2+y^2=100 a function
Answers
Using the function concept, it is found that [tex]x^2 + y^2 = 100[/tex] is not a function, as for each value of x there is more than one corresponding value of y.
Function:In a function, one value of the input can be related to only one value of the output, that is, for each value of x, there can only be one respective value of y.In this problem, the relation is:
[tex]x^2 + y^2 = 100[/tex]
For example, considering x = 0, the corresponding values of y are:
[tex]0^2 + y^2 = 100[/tex]
[tex]y = \pm \sqrt{100}[/tex]
[tex]y = \pm 10[/tex]
Hence, it is not a function, as for each value of x there is more than one corresponding value of y.
To learn more about the function concept, you can take a look at
Write and solve a proportion to answer the question. 3/4 is 75% of what number?
Answers
x = (¾)/75% = (¾)/0.75 = 0.75/0.75 = 1
Answer:
so basically I think it is
¾ = 75%
x = (¾)/75% = (¾)/0.75 = 0.75/0.75 = 1
Step-by-step explanation:
if I am wrong I am so so very sorry
Which statement describes the graph
Answers
Answer:
Your answer is A
Step-by-step explanation:
I hope I helped :)
Joyce Mesnic bought an HP laptop computer at Staples for $699. Joyce made a $100 down payment and financed the
balance at 10% for 12 months. What is her monthly payment? (Round your answer to the nearest cent.)
Answers
599/12= $49.92
suppose you create a graph of the cost function, c=20n + 500 of a new bookstore, and you also graph the revenue function, r=25n, where n is the number of books sold. On your graph, would the point n=150 in the loss section, the profit section, or the break-even section.
Answers
Answer:
Loss section
Step-by-step explanation:
Given
[tex]c = 20n + 500[/tex] -- cost
[tex]r = 25n[/tex] -- revenue
Required
Determine where n = 150 is
To do this, we substitute 150 for n in the given functions
[tex]c = 20n + 500[/tex]
[tex]c = 20 * 150 + 500[/tex]
[tex]c = 3500[/tex]
[tex]r = 25n[/tex]
[tex]r = 25 * 150[/tex]
[tex]r = 3750[/tex]
The above shows that the revenue is greater than cost for n = 150.
This implies that, n = 15o is the loss section.
Answer: profit section :)
PLEASE HELP ME WILL GIVE BRAINLIEST!!!!!!
Answers
Answer:
B
Step-by-step explanation:
Only need to check m:
m^-6 / m^-2 = m^(-6 - -2) = m^-4 = 1 / m^4
Answer:
B
Step-by-step explanation:
solve the system of equations 6x+3y=12 and 5x+y=7
Answers
Solving for x
3(2x+y)=12
2x+y=12/3
2x+y=4
2x=4-y
X=4-y/2
Answer:
x = 1; y = 2
Step-by-step explanation:
To find x:
Multiply (5x+y=7) by 3 to get the y's in both equation the same, and you will get 15x+3y=21.
Now the y's cancel out. Subtract the remaining equations: (15x=21) - (6x=12) and you get 9x = 9. Divide everything by 9 and you get x=1.
To find y:
You can substitute 1 for x in either equation. I will use (5x+y=7).
Substitute the 1 for x: 5(1)+y=7
Simplify: 5+y=7
Put like terms on the same side by subtracting 5 from both sides: y=2
Check:
6(1) + 3(2) = 12
6 + 6 = 12
12 = 12 - this is right
5(1) + (2) = 7
5 + 2 = 7
7 = 7 - this is right
For the sequence tn=n^2-2n,find the third term
Answers
Answer:
t₃ = 3
Step-by-step explanation:
To find the third term substitute n = 3 into the formula, that is
t₃ = 3² - 2(3) = 9 - 6 = 3
Answer:
tn=n^2-2n
n =3
t3 = 3^2 -2(3)
t3 = 9-6
t3 = 3
This graph shows how long, in minutes, it takes Malaya run her miles. How
long does it take her to run 8 miles? *
Answers
Answer:
80 minutes
Step-by-step explanation:
On your graph it says each mile takes 10 minutes. 8 miles take 80 minutes.
What is the solution to x-4≤6?
Answers
Answer:
x - 4 _< 6
Step-by-step explanation:
What does "buying more house than you can afford" mean? Why shouldn't you do this?
Answers
Answer:
Basically it just means that you are trying to spend money that you don't have on things you don't need.
Step-by-step explanation:
Taken literally, you can live in a pretty small house and be content. You don;t need to spend tons of money to be happy. This can be a bad thing to do because you don't want to be in debt to anyone, especially when that could have been avoided.
write an equation through the points (-3,7) and (1,-1)
Answers
The slope is -2.
The slope is the rise over the run. Because the line goes down from left to right, it makes the value negative. For every one the it moves to the right, the line goes down two units.
PLS HELP ME ILL GIVE BRAINLIEST, AND PLS EXPLAIN YOUR ANSWER<3
A field has an area of 9/20 square mile. Determine the width of the field if the length is 9/10 mile long.
Answers
Answer:
[tex] \huge \boxed{ \boxed{ \sf \: \frac{1}{2} }}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:fractionPEMDASequationgiven:area:[tex]\frac{9}{20}[/tex]length:[tex]\frac{9}{10}[/tex]to find:widthtips and formulas:area of a rectangle=l×wlet's solve:let width be w
according to the question
the equation is
[tex] \sf \frac{9}{10 } \times w = \frac{9}{20} [/tex]
let's figure out the equation
[tex] \tt \: divide \: both \: sides \: by \: \frac{9}{10} : \\ \sf\frac{9}{10} \div \frac{9}{10} \times w = \frac{9}{20} \div \frac{9}{10} [/tex][tex] \tt simplify : \\ \sf\frac{9}{10} \times \frac{10}{9} \times w = \frac{9}{10} \times \frac{10}{9} \\ \therefore \: \tt \: w = \frac{1}{2} [/tex]What is the solution to f(x)=g(x) ?
Answers
x=1
Hope this helps!
Joseph has $60 in a savings account. Each week he deposits $12 in the account.
SELECT ALL the expressions that represent the total amount in the account after x weeks.
a.12(5 + 1x)
b.12(5x + 1)
c.60 + 12x
d.6(10 + 2x)
e.60x + 12
f.6(10x + 2)
Answers
Answer:
12x +60
Step-by-step explanation:
c
d
A triangle has two sides of lengths 7 and 9. What value could the length of the third side be? Check all that apply.
Answers
Answer:
A
B
C
E
Step-by-step explanation:
Answer: A, C, E, B I think im PRETTY sure im correct. Maybe 100% sure :)
Which graph can be used to find the solution to the system of equations below? 2x + y = -4 - 3y = 2x + 12 2 -4-3-2-1 -1 1 2 3 5 2. -5 3-2 1 2 1 2 3
Answers
Answer:
F
Step-by-step explanation:
2x+y = -4
put into slope-intercept form: y = -2x - 4
-3y = 2x+12
In slope-intercept form: y = -⅔x - 4
Both equations have a y-intercept of -4. There is only one graph where both lines pass through (0,-4).
The solution of the given system of equation is (0, -4). Therefore, option A is the correct answer.
The given system of equations are 2x+y=-4 and -3y=2x+12.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The system of equations can be solved as follows:
Here, 2x+y=-4 ----------(1)
-3y=2x+12 ----------(2)
From equation(1), y=-4-2x
Now, put y=-4-2x in equation (2) and simplify
That is, -3(-4-2x)=2x+12
⇒ 12+6x=2x+12
⇒ 4x=0
⇒ x=0
Substitute x=0 in equation (2), we get
-3y=12
⇒ y=-4
The solution of the given system of equation is (0, -4). Therefore, option A is the correct answer.
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
#SPJ2
PLEASE ANSWER QUICKLY!
A piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels. Which expression correctly shows the amount remaining in the piggy bank?
Answers
Answer:
The top one
Step-by-step explanation:
In a lab, 100 cells are present at the beginning of an experiment. During the first 10 hours, the number of
cells increased by 28% each hour.
Answers
Answer:
100+0.28*100=100+28=128
Step-by-step explanation:
Pls help I’ll brainlest ASAP
Answers
Answer:
He is 15 years old.
Step-by-step explanation:
I hope this helps :)
Answer:
Artaud is 15 years old
Step-by-step explanation:
Imagine Artaud is x yearrs old.
Now, turning the words in the problem into math equations, we get:
-x + 42 = 27.
Solving for x, we get:
-x = -15
x = 15.
So, Artaud is 15 years old.
What single percentage change is equivalent to a 7% increase followed by a 22% increase
Answers
Answer:
Single increase rate = 29.47%
Step-by-step explanation:
Given:
First increase rate = 7%
Second increase rate = 21%
Find:
Single increase rate
Computation:
Assume number is a
So,
First increase rate = 7%
a + 7%
= 1.07a
Second increase rate = 21%
1.07a + 21%
1.2947a
So,
Single increase rate = 1.2947 - 1
Single increase rate = 0.2947
Single increase rate = 29.47%