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
Someone help me pls
Answers
Answer:
-1 = 2(-1 -1) = -4
0 = 2(0-1) = -2
1 = 2(1-1) = 0
2 = 2(2-1) = 2
Step-by-step explanation:
x = the number on the left column
for the middle colum, you need to do 2(x -1)
for the right column, you do : (x - 1) x 2)
Amana Hagel earns $476 a week. She is married and claims 3 allowances. How much will
be withheld from her weekly paycheck for Federal Income Tax?
Answers
Answer:
$158.67
Step-by-step explanation:
What function is graphed below?
Answers
June earned $ 75 last week. April earned $25. June earnings were how many times greater than April
Answers
Answer:
3 times
Step-by-step explanation:
25 times 3 is 75
This is what i think
pls help (picture) *30 points*
Answers
Answer:
perimeter = 36
Step-by-step explanation:
Each diagonal side is the hypotenuse of a right triangle with legs of lengths 6 and 8.
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10
Each horizontal side measures 8.
perimeter = 8 + 8 + 10 + 10
perimeter = 36
Ellen solved the equation x2−5=59 using the following steps.
Review her work carefully, and then follow the instructions.
Line 1: x2−5=59
Line 2: x2−5+5=59+5
Line 3: x2=64
Line 4: x=8
Which statement identifies a mistake Ellen made, if any?
Answers
Answer:
c
Step-by-step explanation:
In Line 4, she forgot to take the negative square root, because squaring both 8 and −8 equals 64.
Kenny has 8 red shirts, 12 blue shirts, and 10 white shirts in his closet. What is the probability that he would get a white shirt out of the closet?
Answers
Answer:
1/3 or 33.33 %
Step-by-step explanation:
this is because there is 30 shirts and all and 10 white. 10/30 is 1/3, or 33.33%
Answer:
likely
If there are 8 red shirts, 12 blue shirts, and 10 white shirts. The answer would be likely
Hasan plans to choose a book from a section of the store where everything is 25%
off He writes the expression d 0.25d to find the sale price of the book if the original
price is d dollars.
Bella correctly writes another
expression. 0.75d, that will also find the sale price of the
book if the original price is
I/ dollars,
Use the drop-down menus to explain what each part of Hasan's and Bella's
expressions mean.
Answers
Hasan's Expression: d - 0.25d
d: Original price0.25: percent discount 0.25d: amount of discountd - 0.25d: sale price--------------------
Bella's Expression: 0.75d
0.75: percent of original priced: original price0.75d: sale price=============================================
Explanation:
The variable d stands for the original price. The store is offering a 25% sale, which means that Hasan will save 25% of the original price. This means 0.25d represents the amount he saves (aka the discount amount).
For instance, let's say d = 100 is the original price. 25% of this is 0.25d = 25 dollars. So if the book is originally $100, then he saves $25.
As you can probably guess, the 0.75 comes from 1 - 0.25 = 0.75; it indicates that if Hasan saves 25%, then he still has to pay the remaining 75%
Notice how d - 0.25d = 1d - 0.25d = (1-0.25)d = 0.75d which points to the sale price being 75% of the original price d.
Find the value of X Show all work
(2x+6)
36
(4x-18)
Answers
Answer:
X=30
Step-by-step explanation:
(2X + 6) + 36 = (4X- 18)
36=4X-18-2X-6
36=2X-24
2X = 60
X = 30
wELCOME
This is the ANSWER
50 point question Solve quick i will give branliest
Answers
Answer:
17
Step-by-step explanation:
x + 100 = 4x + 49
100 - 49 = 3x
3x = 51
x = 17
Use a protractor to measure the
angle. Then identify it as either
acute, right, obtuse, or straight.
Name
Size
Answers
Answer:
Straight angle 180 degrees
find the value of the angles marked 'x' and 'y'
Answers
Answer:
x=120 y=60
Step-by-step explanation:
Interior angle of a hexagon = 120
Straight line = 180
180-120=60
Whose statement is correct based on the expected value?
Answers
Step-by-step explanation:
only Hadley. and even that is not fully correct.
the expected value here gives us the overall most likely outcome of the scenario when throwing 2 balls.
and not ball by ball. and not directly a probability.
like rolling a die : the expected value of rolling a 6 in 6 attempts is 1 due to the individual roll probability of 1/6.
but the probabilty is NOT 1 or 100% (a guaranteed 6 in 6 attempts).
and that brings me to my concern with Hadley's statement. it says with conviction "the player will make ...". no, only "... will likely make ..." or "... on average".
Answer:
Step-by-step explanation:
neither statement is correct. right answer on khan
For one English test jason correctly answered 22 questions these correct answers gave him a percent score of 50% In total how many questions were on this English test
Answers
What's 9 + 10?
Whoever gets it right get's the crown!
Answers
Answer:
jokes aside it is 19
Step-by-step explanation:
but if it is jokes then 21
Answer:
Step-by-step explanation:
the answer would be 21
(5 1/4−2 1/2)+(6 2/3−3 1/2) plsss help (real answers)
Answers
Answer:
5 11/12. hope this helps
Step-by-step explanation:
Answer:
6
Step-by-step explanation: 5 1/4 - 2/12 = 3 6 2/3 - 3 1/2=3 3+3=6
what are the solutions to the system
Answers
[tex]10+y=5x+x^2~~~~.....(i)\\\\5x+y =1~~~....(ii)\\\\\text{From (i):}\\\\10+y = 5x +x ^2\\\\\\\implies y = 5x +x ^2 -10\\\\\text{Substitute y in equation (ii):}\\\\5x+5x+x^2-10=1\\\\\implies x^2 + 10x -11 =0\\\\\implies x^2 +11x -x -11=0\\\\\implies x(x+11) -(x+11) =0\\\\\implies (x-1)(x+11) =0\\\\\implies x =1 ~~ \text{or}~~ x = -11\\\\\text{Substitute x =~1 in equation (ii):}\\ \\5+y =1 \implies y =-4[/tex]
[tex]\\\text{Substitute}~ x =-11~ \text{in equation (ii):}\\\\\ 5(-11) + y = 1 \implies y = 1 +55 = 56 \\\\\text{Hence} (x,y) = (-11,56) ~~\text{and}~~ (x,y)=(1,-4)[/tex]
jessie works in an electronics store and earns a 7.5% commission on every item that she sells. How much commission would she earn for selling a computer that costs $1,580?
Answers
Work Shown:
7.5% = (7.5)/100 = 0.075
7.5% of $1580 = 0.075*1580 = 118.50
The radius of a circle is 16 ft. Find its area in terms of \pi
Answers
For this problem, first we need to recognize that the area of a circle is found using the equation: pi r^2
When we plug in the value of r:
pi 16^2
We get an answer of 256 pi ft
HELP ME OUT PLEASE!!
For the formula shown, how many sulfur atoms are represented?
O 1
O 2
O 4
O 6
Answers
H₂SO₄ is Sulfuric Acid and the number of atoms Sulfur has is 4 atoms
What is a Chemical Formula?
A chemical formula is a formula that lists the constituent parts of a compound together with their relative proportions. No subscript is used if there is just one atom of a certain kind. A subscript is added to the symbol for an atom if it contains two or more of a certain type of atom.
Given data ,
The chemical is represented as H₂SO₄ which is Sulfuric Acid
Sulfuric acid has 2 atoms of Hydrogen , 1 atom of Sulfur and 4 atoms of Oxygen
As per the chemical formula , we can see that there is no subscript added to the Sulfur S in the chemical formula equation.
Therefore , The number of Sulfur atoms present in H₂SO₄ is 1
Hence , H₂SO₄ has only 1 sulfur atom
To learn more about chemical formula click :
https://brainly.com/question/29031056
#SPJ2
Original Price of a truck $17,100.00 Tax:2.4%
Answers
You multiple the tax by the original to get the amount of tax. Then you add it to your original to get total price.
Answer:
17504.40
Step-by-step explanation:
You take 17100 x 2.4% and get 410.40
add 17100 and 410.40 and get 17504.40
Hi , do you love math ?
Answers
Answer: yes math is so good
Step-by-step explanation:
Each week, Christian earns $x fixing bicycles and receives $10 as his allowance.
To find how much he will earn in total over 2 weeks, Christian calculates the following:
x + 10 + x + 10
What is another way Christian can calculate how much he will earn in total over the 2 weeks?
Drag and drop the equivalent expression in the box.
Answers
Answer:
2(x+10)
Step-by-step explanation:
x + 10 + x + 10 is the same as 2 times the expression x + 10
This can be written as 2(x+10)
-Chetan K
Answer: 2(x+10)
Step-by-step explanation:
x + 10 + x + 10 is the same as 2 times the expression x + 10
This can be written as 2(x+10)
Helps me please help help me
Answers
Answer:
(2, -6)
Step-by-step explanation:
1. The rule for reflecting a point across the y-axis is (x, y) -> (-x, y)
This means that when reflecting across the y-axis, the x-coordinate changes signs.[tex](-(-2),-6)[/tex] [tex](2,-6)[/tex]Therefore, the ordered pair that describes the location of C' is (2, -6).
Answer:
(2, -6)
Step-by-step explanation:
If f(x)=2(x2+5), then f(-3)=
Answers
Answer:
-1
Step-by-step explanation:
So you would do
-3×2= -6
then do
-6+5= -1
1
4
3
Time (h)
2
.
3
Cars
Washed
6
9
12
a. Proportional?
b. Equation:
C. Number of hours:
3. Cars washed:
Answers
Step-by-step explanation:
Proportional = time/cars washed
= 1/3
no. of hours= 90hours
cars washed = 30 cars washed
Hello everybody! Can anybody help me out with this fairly simple multiple choice algebra problem? Thanks!
Answers
Answer:
l = P -2w
________ D is the correct choice
2
3
1) Wendy has 3/5 gallon of milk. She
used 1/8
gallon to make cookies. How
much milk does Wendy have left?
8
a)
T-
WIN
b)
b) io
3
1
19
29
c)
d)
40
40
Answers
Answer: 19/40 gallons
Step-by-step explanation:
She has 3/5. She used 1/8. 3/5=24/40 and 1/8 = 5/40.
24/40 - 5/40 = 19/40 gallons
:0 hope it helps
Anna adds 2oz of milk to an 18oz cup of coffee that is 10% milk. What is the percentage of the milk in the resulting mixture?
Answers
Answer:
19% of milk
lemme know if it helped
Step-by-step explanation:
Help please I’ll give points help help help help
Answers
Answer:
my sample ka
Step-by-step explanation:
bigyan mu ako para masagot ko ang tanong nayan.