What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?

A
(-1, -4)

B
(1, -4)

C
(3, -4)

D
(-3, 12)

Answers

Answer 1

Answer:

  A.  (-1, -4)

Step-by-step explanation:

The vertex can be found by converting the equation from standard form to vertex form.

Vertex

Considering the x-terms, we have ...

  y = (x^2 +2x) -3

where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...

  y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2

  y = (x +1)^2 -4

Compare this to the vertex form equation ...

  y = a(x -h)^2 +k

which has vertex (h, k).

We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).

On the attached graph, the vertex is the turning point, the minimum.

What Are The Coordinates Of The Vertex Of The Parabola With The Equation Y = X2 + 2x 3?A (-1, -4)B (1,

Related Questions

Donna has a $300 loan through the bank she is charged a simple rate The total interest she paid on the loan was $63 As a percentage what was the annual interest rate on her loan

Answers

Answer:

21%

Step-by-step explanation:

($63*100%) / $300 = 21%

Write an inequality for the following statement, 1 is greater than x

Answers

The inequality suitable if 1 is greater than x is x<1.

Given that 1 is greater than x.

We are required to form an inequality which shows that 1 is greater than x.

Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.

It shows the range of quantities.

When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:

x<1

We have not used equal to sign because 1 is greater than x not equal to x.

Hence the inequality suitable if 1 is greater than x is x<1.

Learn more about inequality at https://brainly.com/question/24372553

#SPJ1

DIRE NEED OF HELP, pleaseee help
(not a lot of points sorry)

Answers

Answer:

C. Subtract 4 from both sides.

Step-by-step explanation:

You need the equation in the form x² + ax + b = 0 to then either try factoring or use the quadratic formula.

In order to achieve that, you need to first:

Subtract 4 from both sides.

ASAP help me with this question

Answers

Answer:

SAS and SSA

Kindly award branliest

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.

The criterias that guarantee congruence are :

SSS

SAS

ASA

AAS

[tex] \qquad \large \sf {Conclusion} : [/tex]

Correct options are : b, c, d, e

2(−6c+3)+4c2, left parenthesis, minus, 6, c, plus, 3, right parenthesis, plus, 4, c

Answers

Answer:

[tex]-8c+6[/tex]

Step-by-step explanation:

[tex]2(-6c+3)+4c=-12c+6+4c=\boxed{-8c+6}[/tex]

Answer:

-8c + 6 and 3(-4c+2) + 4c

Step-by-step explanation:

khan

There are three novels on Sam's reading table: Light, Zami, and Money.
. On his next trip, he can choose to take some, none, or all of these novels. In the braces below, list all the possible sets of novels that Sam can take.
Write each set in your list in roster form. If there is more than one set in your list, separate them with commas. If you need the empty set in your list, use the symbol Ø.

Answers

The subsets of the set of novels is given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

How to find the subsets of a set?

Suppose we have a set with cardinality n, that is, with n elements. This set will have 2^n subsets, which are all the possible combinations with the elements of the set, including the empty set.

In this problem, the novels are given as follows:

Light, Zami, and Money.

Hence the possible subsets are given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

With is the list that is asked for this problem, which are the subsets of the set of novels.

More can be learned about the sub-sets of a set at https://brainly.com/question/2000547

#SPJ1

Find the measures of angles x and y

Answers

The angle supplementary to angle b is 132°. So, by the extetior angle theorem, x=165.Angles a and y are supplementary, so y=147.

Ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table given below. General Knowledge Math Science Acel Barek Carlin Acton Bay Acton Anael Max Anael Max Kai Kai Carl Anael Dario Dario Carlin Barek Let G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. Find G n M and G u S .

Answers

The computation shows that:

G n M = Anael and Max

G u S = Acel, Action, Anael, Max, Carl, Dario, Catlin, Kai, and Barek.

How to illustrate the information?

From the information, ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table.

The subjects include general Knowledge Math Science.

Therefore, G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. The intersection is illustrated above.

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

Which of these tables represent a function

Answers

Answer: W

Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .

A circle has a circumference of 50.24 units.
What is the radius of the circle?
Use 3.14 for π and enter your answer as a decimal.
units

Answers

8 units

Circumference = pi * 2 * radius
50.24 = 3.14 * 2 * radius
50.24 = 6.28 * radius
8 = radius

Answer: 8  units

Step-by-step explanation:

Find a formula for the nth term in this arithmetic sequence first term -2 common difference an=

Answers

The formula for the problem is: An = 8(n-1) - 2

Difference of Squares gives which complex factors for the expression +3?
A. (x+3i)(x-3i)
B. (x-i-√3)(x-i√3)
C. (x+3i)^2(x-3i)²
D. (x+i√3)(x-i√3)

Answers

The difference of squares is:

(x+i√3)(x-i√3)

So the correct option is the last one, D.

Which expression gives x^2 + 3?

For a complex number:

[tex]Z = a + b*i[/tex]

We define the complex conjugate of Z as:

[tex]Z' = a - b*i[/tex]

Such that the product between the complex number and its complex conjugate gives:

[tex]Z*Z' = a^2 + b^2[/tex]

Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:

[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]

Which is what we wanted to get, so that is the correct option.

If you want to learn more about complex numbers:

https://brainly.com/question/10662770

#SPJ1

Hey guys I need some help with #11 so if anyone could help that would be great THANK YOU!!

Answers

the answer is (0,-7) !

how you get it:

a=4 , b=0
x=-0/2x4
x=0
f(x)=4x^2-7, x=0
f(0)=-7
(0,-7)

Solve for x

(please write work)

Answers

Answer:

x = -9

Step-by-step explanation:

12 + 2x + 24 = 27 + x

(12 + 24) + 2x = 27 + x

36 + 2x = 27 + x

subtract 27 from both sides

36-27 + 2x = 27-27 + x

9 + 2x = x

subtract x from both sides

9 + x = 0

subtract 9 from both sides

x = -9

(the steps could've been faster but that shows the most work)

check:

12 + 2(-9) + 24 = 27 + (-9)

36 - 18 = 18

18 = 18

True!

so -9 is correct

Answer:

Step-by-step explanation:

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

A line with slope
-1/3
passes through the point (-4, 4).
Find the coordinates of another point on the line.

Answers

Answer:

(0, 8/3) = y-intercept

Step-by-step explanation:

I chose to find the y-intercept since it is easy to find with the given information.

The equation for a line is y = mx + b

To find the y-intercept, we must plug in the info we have and solve for b:

4 = -1/3 (-4) + b

4 = -4/3 + b

8/3 = b

To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:

(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)

How many pairs of parallel faces does this shape have?

Answers

Answer: one

Step-by-step explanation:

parallel faces are the ones that are opposite to each other.

Answer:

one

Step-by-step explanation:

there is only one pair of parallel faces.

Based on the family the graph below belongs to, which equation could represent the graph?

Answers

Considering the asymptotes of the function, the equation that represents the graph is:

[tex]y = \frac{1}{x + 2} + 3[/tex]

What are the asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

This function, from the graph, has a vertical asymptote at x = -2, hence the denominator is given by:[tex]y = \frac{1}{x + 2} + 3[/tex]

x + 2, as x + 2 = 0 -> x = -2.

The horizontal asymptote is of y = 3, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 3[/tex]

Which means that the function is described by the following rule:

[tex]y = \frac{1}{x + 2} + 3[/tex]

More can be learned about asymptotes at https://brainly.com/question/16948935

#SPJ1

Numbers from 1 to 50.
Find the probability of choosing
numbers with last digit 6.

Answers

Answer:

0.1 or 10%

Step-by-step explanation:

The numbers between 1 and 50 that end in 6 are as follows:

6, 16, 26, 36, 46

There are therefore 5 numbers between 1 and 50 that end in 6.

This means there are 5 out of 50, or 5/50.

5/50 is 0.1 as a decimal, or 10% in percentage form.

find derivative of y= sin x sin 3x​

Answers

The derivative of y= sin x sin 3x​ is [tex]$=3 \cos x-3 \cos 3 x$[/tex]

What is a derivative?Futures contracts, options contracts, and credit default swaps are typical types of derivatives. Beyond this, a sizable number of derivative contracts satisfy the requirements of a wide range of counterparties.

To find the derivative of y= sin x sin 3x​:

[tex]$y=3 \sin (x)-\sin (3 x)$[/tex]

[tex]$y^{\prime}=3 \cos x-[\cos (3 x) \cdot 3]$[/tex]

[tex]$y^{\prime}=3(\cos x-\cos 3 x)$[/tex]

[tex]\frac{dx}{dy} =3 cosx - 3 cos x[/tex]

Differentiate [tex]sin 3x[/tex] using the chain rule

Given [tex]y=f^{'} (g(x))*g^{'}[/tex]←chain rule

y=[tex]y=3 sin x-sin 3x[/tex]

[tex]\frac{dx}{dy} =3 cos x - cos 3x*\frac{d}{dx} (3x)[/tex]

[tex]=3cosx-3cos3x[/tex]

To learn more about derivatives, refer to

https://brainly.com/question/23819325

#SPJ9

Underwood Company is preparing its annual profit plan. As part of its analysis of the profitability of individual products, the controller estimates the amount of manufacturing overhead that should be assigned to each of the two product lines from the information given below. Wall Mirrors Specialty Windows Total units produced 30 30 Total number of material moves 7 18 Direct labor hours per unit 145 145 Budgeted material-handling costs are $30,000. The material-handling cost per wall mirror under activity-based costing is:

Answers

The material-handling cost per wall mirror under activity-based costing is $280

What is activity-based costing?

Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.

There 25 materials move in both divisions (i.e. 7+18=25)

Material-handling cost per material move=Budgeted material-handling costs /total material moves

Budgeted material-handling costs =$30,000

Material-handling cost per material move=$30,000/25

Material-handling cost per material move=$1,200

Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move

Total material-handing costs for wall mirror=7*$120

Total material-handing costs for wall mirror=$8,400

material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors

material-handling cost per wall mirror=$8,400/30

material-handling cost per wall mirror=$280

Find out more about   on activity-based costing:https://brainly.com/question/14912137

#SPJ1

Choose the number (X) that should come next in this series (1, 2, 6, 15, X, 56, 92)

Answers

Answer:

31

Step-by-step explanation:

The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31

The unknown number(x) in the series is 31.

The given series 1, 2, 6, 15, x, 56, 92.

We need to find the value of x.

What is a series?

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.

The numbers in the series increase by (n+1)².

So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.

Therefore, the unknown number(x) in the series is 31.

To learn more about the series visit:

https://brainly.com/question/16415816.

#SPJ2

On a map, 3 inches represents 50 miles. Which proportion can be used to find the actual distance represented by 5 inches on the map?
StartFraction 3 over 50 EndFraction = StartFraction x over 5 EndFraction
StartFraction 3 over 50 EndFraction = StartFraction 5 over x EndFraction
StartFraction 3 over x EndFraction = StartFraction 50 over 5 EndFraction
StartFraction x over 3 EndFraction = StartFraction 50 over 5 EndFraction

Answers

The correct proportion that can be used to find the actual distance  represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.

Given that 3 inches on a map represents 50 miles.

We are told to find the proportion which can be used to represent 5 inches.

Multiplication is basically finding the product of two numbers but it can be used to convert the units also.

If 3 inches represents 50 miles then,

1 mile=50/3

Multiply both sides by 5.

5 miles=5*50/3

If we see the options then we will get that the most appropriate and correct option which represents 5 inches is that start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.

Hence the correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.

Learn more about fraction at https://brainly.com/question/78672

#SPJ1

Answer:

B

Step-by-step explanation:

3/50 = 5/x

Suppose follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Answers

Answer:

  c = 2.25

Step-by-step explanation:

The normal distribution function is symmetrical, so the area not in the central zone is split evenly between the lower and upper tails.

Solution

We can find -c from ...

  P(x < -c) = (1 - 0.9756)/2 . . . . .  the area in the lower tail

The calculator tells us -c = -2.25.

  c = 2.25

Given the following function, find f(-5), f(0), and f(3).
f(x) = x^2+5

Answers

Answer:

f(-5) = 30

f(0) = 5

f(3) = 14

Step-by-step explanation:

=> f(x) = x²+5

for , f(-5) = (-5)² +5

=> 25 +5

=> 30

for , f(0) = (0)² +5

=> 5

for , f(3) = (3)² + 5

=> 9 + 5

=> 14

which table of ordered pairs represents a proportional relationship?

Answers

Answer:

B

Step-by-step explanation:

Every (x,y) pair is equal to each other, thus making them proportional :)

(Subtracting rational coefficients-Mixed numbers)

Simplify by combining like terms:

1/3k - 8 3/4k

[?] ?
_k
?

Answers

Answer:

-8 5/12

Step-by-step explanation:

A rectangular box is designed to have a square base and an open top. The volume is to be 500in.3 What is the minimum surface area that such a box can have?

Answers

The minimum surface area that such a box can have is 380 square

How to determine the minimum surface area such a box can have?

Represent the base length with x and the bwith h.

So, the volume is

V = x^2h

This gives

x^2h = 500

Make h the subject

h = 500/x^2

The surface area is

S = 2(x^2 + 2xh)

Expand

S = 2x^2 + 4xh

Substitute h = 500/x^2

S = 2x^2 + 4x * 500/x^2

Evaluate

S = 2x^2 + 2000/x

Differentiate

S' = 4x - 2000/x^2

Set the equation to 0

4x - 2000/x^2 = 0

Multiply through by x^2

4x^3 - 2000 = 0

This gives

4x^3= 2000

Divide by 4

x^3 = 500

Take the cube root

x = 7.94

Substitute x = 7.94 in S = 2x^2 + 2000/x

S = 2 * 7.94^2 + 2000/7.94

Evaluate

S = 380

Hence, the minimum surface area that such a box can have is 380 square

Read more about surface area at

https://brainly.com/question/76387

#SPJ1

a population of bobcats increase by 5% per year if the population is currently 40 in how many years will the population reach 80 round your answer to the nearest tenth. The population will reach 80 in about _____years​

Answers

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & 80\\ P=\textit{initial amount}\dotfill &40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 80=40(1 + 0.05)^{t}\implies \cfrac{80}{40}=1.05^t\implies 2=1.05^t\implies \log(2)=\log(1.05^t) \\\\\\ \log(2)=t\log(1.05)\implies \cfrac{\log(2)}{\log(1.05)}=t\implies 14.2\approx t[/tex]

27. Identify the domain of the set (6,2), (-1,-5), (4,4), (9, 2) and tell if the relation is a function.
O {-1, 4, 6, 9); not a function
O {-5, 2, 4}; a function
O {-1,4,6,9}; a function
O {-5, 2, 4); not a function

Answers

Answer:

the third one

Step-by-step explanation:

it is function that contain four domain

Find f. f ″(x) = x^−2, x > 0, f(1) = 0, f(6) = 0

Answers

If you do in fact mean [tex]f(1)=f(6)=0[/tex] (as opposed to one of these being the derivative of [tex]f[/tex] at some point), then integrating twice gives

[tex]f''(x) = -\dfrac1{x^2}[/tex]

[tex]f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1[/tex]

[tex]f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2[/tex]

From the initial conditions, we find

[tex]f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0[/tex]

[tex]f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)[/tex]

Eliminating [tex]C_2[/tex], we get

[tex](C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))[/tex]

[tex]-5C_1 = \ln(6)[/tex]

[tex]C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)[/tex]

Then

[tex]\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}[/tex]

Other Questions
HELP WITH MATH PLS!!!!! describe the types of colonial schools and explained who attended them? After a customer has purchased a refrigerator, he was offered free delivery, installation, financing, and warranty. this is known as the _________ Which of the following represents all solutions to the equation 1/3x^2 +10 = 7 Mrs. Greenaway has decided to open a new preschool in her town. To decide whether she will have enough students to be successful, she hires a researcher to conduct a survey of the towns population. Which of the following groups would make up the best sample for this survey? A. parents of preschool children B. parents of elementary school children C. registered voters in the town D. members of the town council The most common viral syndrome of pericarditis, myocarditis, and pleurodynia (pain upon breathing) is caused by:________ How does the dynamic model of aggregate supply and aggregate demand explain inflation? Which line of best fit accurately represents the given scatter plot? Please help with this qn :) The sum of the length of a side of two squares is 18cm and the sum of their areas is 212 cm^2. find the length of a side of the smaller square The organization whose mission is to improve the health of the public and achieve health equity is the :_______ In the reaction hc2h3o2 h2o------>c2h3o2 - h3o , which substance is bronted -lowrey base? Distinguish between a correlation and an autocorrelation. how are these measures similar? how are they different? In the expansion of (2a + 3b)8, which of the following are possible variable terms? Explain your reasoning.a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5 Solve the system of equations algebraically and create a graphical model.[tex]3x + 2y = 8 \\ x + 2y = 4[/tex] Conversion Chart5 milliliters=1 teaspoon768 teaspoons = 1 gallon1 gallon = 4 liters1000 milliliters=Calculate the area affected if the following ships were involved in an accident & spilled their oil:A tanker truck holding 8,000 gallons or 32,000 liter.A ship holding 300,000 gallons or 1.2 million liters.A supertanker holding 83,000,000 gallons or 332 million liters.2. How could an oil spill affect bird nesting near the contaminated body of water? In a population where 81 % of voters prefer Candidate A,an organization conducts a poll of 15 voters. Find theprobability that 11 of the 15 voters will prefer Candidate [tex]\lim_{x \to 0 (\frac{x(x-2)}{2-2e^2x} )[/tex] Help evaluting this limit Someone please help me with Graph!!(My answers keep coming wrong)Topic= Solving systems of equations by Graphing Solve the equation in the image (yr 8 math, 40pt) Many companies use ________ to customize koozies for customers to use as inexpensive promotions.