Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x, y) point.
y= -x^2-10x-22
Answers
Answer:
vertex: (-5, 3)
Step-by-step explanation:
Besides providing the graph of the given quadratic equation, I will also demonstrate the algebraic method of solving for the vertex of a parabola.
Method 1: Algebraic SolutionGiven the quadratic equation, y = -x² - 10x - 22, where:
a = -1, b = -10, and c = -22.
Find the x-coordinate of the vertex:In order to find the vertex of the given equation, use the following formula to find the x-coordinate of the vertex: [tex]x = \frac{-b}{2a}[/tex].
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{-(-10)}{2(-1)}[/tex]
[tex]x = \frac{10}{-2}[/tex]
x = -5
The x-coordinate of the vertex is: x = 5.
Find the y-coordinate of the vertex:Next, substitute the value of the x-coordinate into the given quadratic equation to find its corresponding y-coordinate:
y = -x² - 10x - 22
y = -(-5)² - 10(-5) - 22
y = -25 + 50 - 22
y = 3
Therefore, the vertex of the given parabola is: (-5, 3), where it is the maximum point.
One of the attachments is the screenshot of the graphed quadratic equation (using Desmos), where it shows the vertex as the maximum point.
Method 2: Graphing CalculatorIf you have a graphing calculator (such as the Texas Instruments graphing calculator):
Press Y=Then, simply enter the given quadratic equation, -x² - 10x - 22.Next, press 2ND ⇒ Quit. Press the GRAPH button. Press 2ND ⇒ TRACE Select option 4: maximumIt will ask for the "Left Bound?": move the cursor as close to the maximum point as possiblePress ENTER. Next, it will ask for the "RightBound?" Repeat the same process as in step #7. Press ENTER.It will ask for "Guess?" ⇒ press ENTER, and it will provide the same coordinates for the vertex, (-5, 3).Please let me know if you have any questions or concerns regarding this post.
Related Questions
p l s… h e l p… m e…
Match the unknown entries in the two matrices with their correct values
Answers
Answers:
v = 54y = 0u = 6w = -48x = -1===================================================
Explanation:
The left hand side is
[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}[/tex]
That -6 outside the matrix is multiplied with each item inside the matrix. This is known as scalar matrix multiplication. Effectively, it's very similar to the idea of the distributive property.
So for the first row, we have the three columns of: -6*3 = -18 and -6*(-1) = 6 and -6*3 = -18
The other two rows are handled the same way. This is what should result:
[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}= \begin{bmatrix}-18 & 6 & -18\\-48 & -6x & 54\\-24 & 6 & -6y\end{bmatrix}[/tex]
From here, you'll then match up the terms in the given right hand side matrix. The top row has the variable 'u' in the middle, which matches with the '6' in the middle of the top row shown. Therefore, u = 6.
-----------------------------
Now to the second row.
The -48 in the first spot pairs up with the w in the other matrix. So we can see that w = -48. Similarly, we have v = 54.
Also, we have -6x in the middle which matches with the 6 in the same corresponding spot. Solving -6x = 6 leads to x = -1.
-----------------------------
Finally, the third row.
There's only one variable here and that's the variable y in the bottom right corner. It pairs up with 0 in the same corresponding spot for the right hand side matrix. Therefore, y = 0.
how many times can 2 go into 67
fourth grade help
Answers
Answer:
Step-by-step explanation:
To answer this, divide 67 by 2, writing the answer as a mixed number:
67
---- = 33 1/2
2
thus, 2 can go into 67 33 times, keeping in mind that there's a remainder (1/2).
Math experts please simplify this thank you
Answers
Answer:
t+4 / t-4
Step-by-step explanation:
(t^2 - 16) / (t^2 -8t +16)
=( t^2 - 4^2) / (t^2 - 2*4*t + 4^2)
by formula a^2 - b^2 = (a+b)(a-b)
= (t+4)(t-4) / (t-4)^2
= (t+4)(t-4) / (t-4)(t-4)
= t+4 / t-4
The table shows a linear relationship between x and y.
x
-6
-3
1
4
Y
21
13.5
3.5
-4
What is the slope of the line represented by the values in the table?
Answers
Hope this helps!! :)
I need a help.... thankyouu to those who can ans. this:))
A. BSA Method
B. Clark's Rule
(20 points)
Answers
A
Step-by-step explanation:
just trust me that is the correct answer
To find the equation of a regression line, ý = ax + b, you need these formulas:
8=13
--
b= y - az
S
A regression line has a slope of 2.334. If the mean of the x-coordinates of the
data points is 6.607, and the mean of the y-coordinates is 10.738, what is the
y-value of the y-intercept of the line to three decimal places?
A. -18.455
B. -4.683
C. 4.683
D. 18.455
Answers
Answer:-4.683
Step-by-step explanation:
Took the test
What is the simplified form of the expression? 7r - 8r + 13 -2r + 5? Please help me
Answers
Answer:
- 3r + 18
Step-by-step explanation:
7r - 8r - 2r + 13 + 5 = 7r - 10r + 18
9. Machine Trades Find the width X of the V-thread shown. (Round to the
nearest thousandth.)
Answers
Answer:
X would be 1,000
Step-by-step explanation:
Emily sells her books through Amazon. She makes a profit of $3 per book sale, however, she needs to pay $6 to Amazon Pay in fees for using their app. How many books would she need to sell to make a profit of at least $120 per day?
Answers
Answer:
Step-by-step explanation:
ASSUMING the usage fees are daily fees
120 = 3x - 6
126 = 3x
x = 42 books
d = 10.2 ft, r = 0.5 ft/h
Answers
Answer:
20.4
Step-by-step explanation:
If you are using D = r × t
10.2 = 0.5(t)
10.2/0.5 = t
20.4 = t
Answer:
20.4
Step-by-step explanation:
Q
1). 20² + 20^2
nt : I from is Indonesian
Answers
Answer:
[tex]\red{\rule{4pt}{700000pt}}[/tex]
Step-by-step explanation:
hi
7x+3y=m, solve for y
Answers
We need to subtract 7x on both sides
Then divide the entire thing by 3
Carla and Diane Bought identical suit cases at a different stores. Carla’s suitcase originally cost $85 and was on sale for 20% off the original price which suitcase was a the better deal? What do we know ? List important facts ? What do we want to find out ?? Solve ??? Show ur work? Explain starts ur Asnwer and give details ? And justify your steps ?
Answers
Answer:
Carla's was the better deal with $68.00
Diane's: $85.00
Step-by-step explanation:
0.2 x 85 = 17
85 - 17 = 68$
please i need help
How many rows of seats are inside the theater? Enter your answer in the box.
Answers
Answer:
24 rows
Step-by-step explanation:
384 seats in total, and 16 chairs in a row, so 384/ 16=
24 rows
Hope this helps!
LMK if it does
On a map 1 inch equas 27 miles. How much is 3 inches
Answers
Answer:
3 × 27
=81
mark BRAINLIEST pls
Samuel wants to use his earnings from Monday and Tuesday to buy some batteries that cost 5.60 each how many batteries can samuel buy
Answers
Answer:
i cannot answer this because i do not know hw much money he has made.
Step-by-step explanation:
17. Which of the following numbers is the largest. Explain why you made the choice you did.
-3/4, -3/2,-1, -2/3
Answers
Answer:
3/1
Step-by-step explanation:
because why not
If x^2 - (3x-a) (bx-1) = c, where a, b, and c are constants, what id the value of c?
A. 9
B. 7
C. 13
D. 2
Answers
Identify this function
f (x) =x
Answers
Answer:
linear
Step-by-step explanation:
Find all the square roots of 36
Answers
Hey there!
√36
= √6^2
= 6
Therefore, your answer should be: 6
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Step-by-step explanation:
[tex] \sqrt{36} = ...[/tex]
[tex] = {36}^{ \frac{1}{2} } = (6 {}^{2} ) {}^{ \frac{1}{2} } [/tex]
= 6
Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
f(x)=2(x−8) ^2−3
Answers
Answer:
It's a minimum, at (8, -3)
Step-by-step explanation:
Option 1: you unwrap the square , add like terms, and then recognize it's a parabola and find the coordinates of the vertex.
Or look at it as -3 + something ^2. It means you are adding something positive to -3, so the sum is greater or equal to -3, that is the definition of a minimum. At that point you find the minimum by setting that something equal to 0 (which gives you x = 8) and the value is -3 + 0 = -3
Decide where the first digit of the quotient should be placed without performing division The first digit of the quotient for 2,370 = 24 should be in the Choose... ones tens hundreds thousands
Answers
Answer:
tens place
Step-by-step explanation:
24 can't be into the thousands place or the hundreds place. hope this helps
Answer
hundredths place
Step-by-step explanation:
When performing long division, the first digit of the quotient appears over the least significant digit of the first portion of the dividend that is greater than or equal to the divisor.
Here, when performing long division we compare ...
64 vs 1 . . . no quotient digit
64 vs 15 . . . no quotient digit
64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, 2 in the hundredths place.
There are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen
Answers
Answer:
45
Step-by-step explanation:
This is a combination question: how many ways can you pick 2 people from a group of 10?
Using the notation C(10, 2) for the number of combinations of 10 things chosen 2 at a time...
[tex]C(10, 2)=\frac{10!}{2!(10-2)!}=\frac{10!}{2!\cdot 8!}=\frac{10\cdot 9}{2\cdot 1}=45[/tex]
A car is traveling at a speed of 54 kilometers per hour. What is the car's speed in meters per second? How many meters will the car travel in 10 seconds? Do not round your answers.
Answers
An electrician charges a rate of $60 per hour plus a fee of $35 per job. Which expression represents the electrician's hourly rate?
60 + 35h
Answers
The hourly rate is 60, so multiply 60 by the number of hours (h) and add the fee:
Answer: 60h + 35
100÷5+25×3=
AYUDAA ES PARA HOYYY
Answers
Answer:
95
Step-by-step explanation:
100 divided by 5 plus 25 times 3 is 95 :)
100/5=20
25x3=75
75+20=95
95
You need 1 1/4 cups of sugar to make 20 cookies. To make 16 cookies you will need how much sugar?
Answers
Answer:
You need 1 cup of sugar.
Step-by-step explanation:
16/20 = 4/5
1 1/4 = 5/4
5/4 x 4/5 = 1
You need 1 cup of sugar.
Please help if you can!
Answers
Answer:
-3
Step-by-step explanation:
that’s where the line intercepts with the y axis
Answer:
-3,0 is y intercept good luck
A sunflower is 13 inches tall and grows 41 inches each month. The
sunflower's height is a linear function of time. Which statement best
describes the rate of change and initial value of this function?
A. The rate of change is the number of inches grown per month, and
the initial value is the first month.
B. The rate of change is the number of inches grown per month, and
the initial value is the starting height.
C. The rate of change is the starting height, and the initial value is the
number of inches grown per month.
D. The rate of change is the number of months per inch grown, and
the initial value is the first month.
Answers
Answer:The rate of change is the number of inches grown per month, and
the initial value is the starting height.
Step-by-step explanation:
The rate of change is the starting height, and the initial value is the
number of inches grown per month.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept
Given,
A sunflower is 13 inches tall and grows 41 inches each month.
The sunflower's height is a linear function of time.
A linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
y=13+41x.
Here x represents the number of months
13 is the initial height of the sunflower.
In the given options, The rate of change is the starting height, and the initial value is the number of inches grown per month is the statement best describes the rate of change and initial value of this function
Hence, The rate of change is the starting height, and the initial value is the number of inches grown per month
To learn more on slope intercept form click:
https://brainly.com/question/9682526
#SPJ2
Explain how you can write 4.1 as a/b
Answers
Answer:
ax + by
Step-by-step explanation:
i hope its correct
if its wrong then im sorry :)