leirbe the vector with magnitude |vi|l = 89.5 at an angle of 305° from the positive x axis. Find the component form of vector v.
a) v=<-73.3,51.3>
b) v=<73.3,-51.3>
c)v=<-51.3,73.3>
d) v=<51.3,-73.3>

Answers

Answer 1

The required component form of the vector V is given as  v=<51.3,-73.3>. Option D is correct.

What is vector?

Vector is defined as property of object that describes both magnitude and direction of object when in motion is called vector.

here,
|V| = 89.5
and Ф = 305
now,
x component = |V| cos305°
                    = 89.5×cos305° = 51.3

y component =  |V| sin305°

                    = 89.5×sin305° = -73.3

Thus, the required component form of the vector is given as  v=<51.3,-73.3>. Option D is correct.

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Related Questions

Find the area of the shaded region.

Answers

Answer:

  18π cm² ≈ 56.5 cm²

Step-by-step explanation:

The area of the sector can be found using an appropriate area formula.

Sector area

When the sector central angle is given in radians, the formula for the area of that sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius

When the angle is in degrees, the formula will include a factor to convert it to radians:

  A = 1/2r²θ(π/180) . . . . where angle θ is in degrees

  A = (πθ/360)r² . . . . simplified slightly

The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...

  A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²


Jason deposited $18 000 in a bank that offers an interest rate of 5% per annum compounded
daily.
He kept the money in the bank for 20 days, before withdrawing an amount, H.
Given that, the balance in the bank after another 20 days is $16 093.41, find H.

Answers

Answer:

$1995.97.

Step-by-step explanation:

Amount in bank after 20 days =

18000(1 + 0.05/365)^20

= $18049.38

So H = 18049.38 - 16093.41

        =  $1995.97.

Which logarithmic equation correctly rewrites this exponential equation? 8x = 64

Answers

The logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

How to determine the logarithmic equation?

The exponential equation is given as:

8^x = 64

Take the logarithm of both sides

xlog(8) = log(64)

Divide both sides by log(8)

x = log(64)/log(8)

Apply the change of base rule

[tex]x = \log_8(64)[/tex]

Hence, the logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

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2. What is the domain and range of the
graph shown?
-8-64
10-
8-
B
4+
2-
4+
6+
do do t
-10
2 4 6 8 10 12

Answers

Answer:

domain: x ≥ 0range: y ≥ 0

Step-by-step explanation:

The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.

Domain

The domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).

Range

The range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).

14. Kathy lives directly east of the park. The football field is directly south of the park. The library (1 point) sits on the line formed between Kathy's home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 9 miles from her home. The football field is 12 miles from the library.

Park

Home

9 miles

Library

12 miles

Football field

a. How far is the library from the park?

b. How far is the park from the football field?

6.√3 miles; 6.7 miles

6.7 miles: 6.3 miles

√33 miles. √21 miles

√21 miles, √33 miles

Answers

Answer:

  (a)  6√3, 6√7

Step-by-step explanation:

The right triangles shown are all similar, so corresponding sides are proportional. This gives rise to three "geometric mean" relations between the various lengths.

Geometric mean relations

Using P, F, L, and H to represent the points marked Park, Football field, Library, and Home, the relations are ...

  PF/FH = FL/PF   ⇒   PF = √(FH·FL)

  PL/FL = HL/PL   ⇒   PL = √(FL·HL)

  PH/HL = HF/PH   ⇒   PH = √(HL·HF)

Application

(a) The distance from the park to the library is ...

  PL = √(FL·HL) = √(12·9) = 6√3 . . . miles

(b) The distance from the football field to the park is ...

  PF = √(FH·FL) = √(21·12) = 6√7 . . . miles

K
Use the commutative law of multiplication to write an
14+ ab
equivalent expression.
....

Answers

Applying the commutative law to our question, we have; 14 + ab = ab + 14

How to use the commutative law?

The commutative law in algebra states that the change in position of two numbers while adding or multiplying them does not change the result. For example;

ab + cd = cd + ab

similarly, fg * jk = jk * fg

Applying the above commutative law to our question, we have;

14 + ab = ab + 14

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help....
delta math questions...

Answers

The length of BD is √182

How to solve for x?

The given parameters are:

AD = 7

DC = 26

BD = x

The side lengths are represented by the following ratio:

7 : x = x : 26

Express as fraction

7/x = x/26

Cross multiply

x^2 = 182

Take the square roots

x = √182

Hence, the length of BD is √182

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Answer:

The length of BD is √182

hope this helps :)

A deck of 52 cards contains an equal amount of hearts, diamonds, clubs, and spades. If one card is picked at random from the deck, the probability that it is a club is:

a)1/52
b)1/13
c) 1/10
d) 1/4

Answers

Answer: B) 1/13

Step-by-step explanation:

There are 52 cards. So, there are 52/4 = 13 cards of each amount of hearts, diamonds, clubs and spades. In this case, we're looking for the probability of picking a club. Since there are 13 club cards and we want to know the probability of picking ONE, our answer is b) 1/13.

Considering the definition of probability, the correct answer is option d): if one card is picked at random from the deck, the probability that it is a club is 1/4.

Definition of probability

The higher or lower possibility that a particular event will occur is known as the probability. This is, the probability establishes a relationship between quantity of favorable events and the total quantity of possible events.

The ratio of favorable situations (the number of cases in which event A may or may not occur) to all possible cases is used to calculate the the probability of any event A. This is called Laplace's Law:

probability= number of favorable cases÷ total number of possible cases

Probability that the picked card is a club

In this case, you know:

Total number of cards = 52 (number of possible cases)The deck of cards contains an equal amount of hearts, diamonds, clubs, and spades.Total number of cards that are clubs= 52÷4= 13 (number of favorable cases)

Replacing in the definition of probability:

probability= 13÷ 52

Solving:

porbability= 1/4

Finally, if one card is picked at random from the deck, the probability that it is a club is 1/4.

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Pls help with b

The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.

a. Angle a = 72.54 degrees

b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys

Answers

The length of a taut belt around the two pulleys is 79.3 cm.

Length around the pulley

The length of a taut belt around the two pulleys is calculated as follows;

Shapes formed within the two circles of the pulley.

From top to bottom, a rectangle, a right triangle and a trapezium.

Length of the rectangle

The height of the right triangle is equal to length of the rectangle

base of the right triangle = radius of big circle - radius of small circle

base of the right triangle = (0.5 x 12 cm) - (0.5 x 6 cm) = 3 cm

tan α = height/base

tan (72.54)  = h/3

h = 3 tan(72.54)

h = 9.54 cm

Length of trapezium at bottom

The length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm

Angles and length of belt in each circle

Portion of belt in contact with circumference of small circle is subtended by an angle = 2 × 72.54 = 145.08°

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 6 cm)π x (145.08/360)

= 15.19 cm

Portion of belt in contact with circumference of big circle is subtended by an angle = 360 - 145.08° = 214.92⁰

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 12 cm)π x (214.92 / 360)

= 45.01 cm

Length of a taut belt around the two pulleys

= 9.54 cm + 9.54 cm + 15.19 cm + 45.01 cm

= 79.28 cm

= 79.3 cm

Thus, the length of a taut belt around the two pulleys is 79.3 cm.

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See picture to answer!

Answers

Using the law of cosines, it is found that the length of side AB is of AB = 13.

What is the law of cosines?

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

c is the length of the side opposite to angle C.a and b are the lengths of the other sides.

For this problem, the parameters are:

C = 120, a = 8, b = 7.

Hence:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]

[tex]c^2 = 169[/tex]

[tex]c = \sqrt{169}[/tex]

c = 13.

Hence AB = 13.

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graph the following system of inequalities. y ≤ 1 3 ⁢ x − 2 x < 4

Answers

By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

How to graph a system of inequalities?

An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).

Given the following system of inequalities:

y ≤ 1/3x  ⇒ y - 1/3x ≤ 0

y - 2x < 4

By using an online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

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Complete Question:

Graph the following system of inequalities.

y ≤ 1/3x and y - 2x < 4

please help with these 3 questions

Answers

Answer:

1. D) Both b) and c)

2. B) Cosine Law

3. B) Find the measures of angles and sides that we can't physically measure.

Step-by-step explanation:

1. To solve non-right triangles we use Sine Law and Cosine Law.

2. If 3 sides lengths were given and you were asked to find an angle, you would use the Cosine Law.

3.Trigonometry is used in real life to find the measures of angles and sides that we can't physically measure.

On a coordinate plane, quadrilateral D G A R is shown. Point G is at (negative 8, 3), point A is (4, 8), point R is at (10, 0), and point (negative 2, negative 5).

A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden.

The perimeter of his garden is

meters.

Answers

The perimeter of the garden is 46 units.

How to calculate the perimeter?

To calculate for the perimeter of the garden, we have to solve for the measures of each of the sides of the four-sided polygon. That is calculated by getting the distances between consecutive points.

The equation for the distance is:

d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)

Distance from G and A,

d = sqrt ((4 - -8)² + (8 - 3)²)

d = 13

Distance from A to R,

d = sqrt ((10 - 4)² + (0 - 8)²)

d = 10

Distance from R to D,

d = sqrt ((-2 - 10)² + (-5 - 0)²

d = 13

Distance from D to G,

d = sqrt ((-8 --2)² + (-5 -3)²)

d = 10

Summing up all the four calculated distances will give us an answer of 46.

Thus, the perimeter of the garden is 46 units.

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Answer: 46 meters.

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

What is the equation of the line through the origin and (-2,3)?

Answers

Step-by-step explanation:

[tex]algenbraic[/tex]

The following is a 3-step proof. Complete the proof.

Given: 1 = 2

AP = BP

Answers

1) [tex]\angle 1=\angle 2[/tex], [tex]AP=BP[/tex] (given)

2) [tex]\angle APD=\angle BPC[/tex] (vertical angles are equal)

3) [tex]\triangle ABD \cong \triangle BAC[/tex] (ASA)

The steps to derive the quadratic formula are shown below:


Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4


Provide the next step to derive the quadratic formula.
x squared plus b over a times x minus quantity b over 2 times a all squared equals negative c over a minus quantity b over 2 times a all squared
x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared
x squared plus b over a times x minus quantity 2 times a over b all squared equals negative c over a minus quantity 2 times a over b all squared
x squared plus b over a times x plus quantity 2 times a over b all squared equals negative c over a plus quantity 2 times a over b all squared

Answers

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Step-by-step explanation:

Step 3:

[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)

The next step will be:to find the b² for the expression on the left.How to find b²:

Take the expression

[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]

We can also write it as:

[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]

According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,

b² will be:

[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]

So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)

For STEP 4, the equation will become:

[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The next step is to divide b/a by 2 then square it and add to both sides.

This creates a perfect square quadratic on left side.

So the answer is :

x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared

Evaluate

I don’t know how to type this out so I have the photo

Answers

Answer:

3.959797975

Step-by-step explanation:

1. Find the square root of 98 which is 9.899494937

2. Divide 9.899494937 by 2.5 which is 3.959797975

(sorry if it's wrong, but I think it's correct)

The average weight of full-grown beef cows is 1,470 pounds with a standard deviation of 230 pounds. if the weights are normally distributed, what is the percentile rank of a cow that weighs 1,750 pounds? (1) 89th (2) 76th (3) 49th (4) 35th

Answers

Answer: The percentile is 89

Step-by-step explanation:

This question can be solved using concept for t tables

In a normal distribution the curve. [tex]\mu= 1470 , \sigma = 230, x=1750[/tex]

The relationship between z score, mean and standard deviation is given by

[tex]x = \mu+z\sigma[/tex]

So the z value according to this is given by the formula

[tex]1750=1470+z(230)\\ z=\frac{280}{230} \\\\z = 1.217[/tex]

From the z table we can infer that p value for z=+1.217 is 88.82

So 1750 is 89th percentile

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What is the volume of this rectangular prism?
3/2cm
1/2
4 cm

Answers

Answer:

7.62

Step-by-step explanation:

length* width* height = 3/2*1/2*4=7.62 cm

Can you please solve this I need help

Answers

Answer:

7k - 7

Step-by-step explanation:

- k - (- 8k + 7) ← distribute parenthesis by - 1

= - k + 8k - 7 ← collect like terms

= 7k - 7

The product of two powers is 11^8 and their quotient is 11². What are the two powers? Explain.

Answers

Answer:

The powers are 3 and 5.

Step-by-step explanation:

When you multiply 2 exponential functions you add the powers and when you divide these functions you subtract the powers, so we have:

11^a * 11^b = 11^(a+b)

11^a/ 11^b = 11^(a-b)

So, from the information given:

      a + b = 8

      a -  b = 2       Adding:-

    2a = 10

     a = 5.

and substituting in the second equation

   5 - b = 2

         b = 3.

   

You decide to buy a laptop for $750. You make a down payment of $150 and the company will allow you to pay off the remainder in 12 payments over the next year at 13.5% interest with a finance charge of $25. Make a table of all payments over the next year including the initial down payment and finance charge. Show the difference between paying in cash for the laptop and this financial arrangement. Show all equations and calculations you used. Explain the benefits and downsides of financing your laptop and describe when you would advise someone to finance this kind of purchase. Upload your payment table and answers below.

Answers

Total amount paid over the next year including the initial down payment and finance charge = $856

The difference between paying in cash for the laptop and this financial arrangement = $106

Cost of laptop=$750

Down payment=$150

Finance charges = $25

Remaining amount =$600

Amount for 1 month including 13.5 % interest=600/12*13.5/100+600/12

                                                                       =$56.75

Total amount paid over the next year including the initial down payment and finance charge =  56.75*12+150+25 = $ 856

The difference between paying in cash for the laptop and this financial arrangement = $106

Benefits of financing laptop:

A costly laptop can be yours without having to pay in full.

Bank loans and conventional credit card services are not required.

Numerous retailers provide rewards, flexible payment plans, zero-interest rates, and other benefits.

Downsides of financing laptop:

It's dangerous to borrow money because late payments might result in fees and excessive interest rates.

A credit score may suffer if there is no interest charged.

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What catergory does -36/12 belong in

Answers

Answer:

Improper fraction

Step-by-step explanation:

-36/12 is indeed an improper fraction. An improper fraction is usually a fraction where the numerator is larger than the denominator. Which in order for the fraction to be a "proper" fraction, the fraction has to have a numerator that is smaller than the denominator. Not only is this fraction an improper one, but it can also be heavily reduced (or simplified) by dividing the numerator/denominator by a common factor, which you would still have an improper fraction speaking how the numerator will still be greater than the denominator.

Hope this helps.

Answer:

Proper Fraction

Step-by-step explanation:

Some band members have raised much more money than other. which measure can be used to show this?explain.

Answers

A ratio measure can be used to show this.

What is a ratio measure?A ratio in mathematics describes how many times one number contains another.The highest (most sophisticated) level of measurement that a variable can have is referred to as a ratio measure.A 3 to 5 ratio (3:5) A 3:5 ratio can be written as 3:5, 3/5, or 3/5. Furthermore, 3 and 5 can represent any number or measurement, including pupils, fruit, weights, heights, speed, and so on. A 3 to 5 ratio simply means that for every three of something, there are five of something else, for a total of eight.

Therefore, a ratio measure can be used to show the given situation.

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Write the equation of the transformed graphs of each trigonometric function

Answers

The equations of the transformed graphs are [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex] and [tex]y = -\frac34\sin(2x)[/tex]

How to transform the functions?

The tangent function

The parent function is:

y = Atan(Bx) + k

It has a period of 4.

So, we have:

[tex]\frac{\pi}{B} = 4[/tex]

Make B the subject

[tex]B = \frac{\pi}{4}[/tex]

It is shifted vertically up by 3 units.

So, we have:

k = 3

Substitute these values in y = Atan(Bx) + k and remove A

[tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]

Hence, the equation of the transformed graph is [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]

The sine function

The parent function is:

y = Asin(Bx) + k

It has a period of [tex]\pi[/tex]

So, we have:

[tex]\frac{2\pi}{B} = \pi[/tex]

Make B the subject

B = 2

It has an amplitude of 3/4

So, we have:

A = 3/4

It is flipped across the x-axis

So, we have:

A = -3/4

Substitute these values in y = Asin(Bx) + k and remove k

[tex]y = -\frac34\sin(2x)[/tex]

Hence, the equation of the transformed graph is [tex]y = -\frac34\sin(2x)[/tex]

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What is the domain of the function shown on the graph?

Answers

Answer:

domain {x:x-2}

or in interval notation [-2,)

Circle C is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is 36 degrees, and the second arc formed is 106 degrees.

In the diagram of circle C, what is the measure of ∠1?
17°
35°
70°
71°

Answers

The measure of the ∠1 is 35 degrees.

How to determine the angle

it is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.

Also, the angle subtended by the arc at the center of the circle is the angle of the arc

From the diagram, we have

m ∠ of external angle = half of the difference of arc angles

The arc angles are

106°36°

m ∠ of external angle = ∠ 1

Let's substitute the angles

∠1 = [tex]\frac{106 - 36}{2}[/tex]

∠ 1 = [tex]\frac{70}{2}[/tex]

∠ 1 = 35°

We can see that the external angle 1 measures 35 degrees.

Note that the complete image is added.

Thus, the measure of the ∠1 is 35 degrees.

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Which expression represents the product of ³ + 2x - 1 and 4 -³ +3?
I7-214-3
1¹+2x+2
1¹2-1⁹ +²+2x³ +6x-3
27-26 +225-3x² + 4x³ + 6x - 3
Don

Answers

The expression that gives the product of the polynomials x³ + 2x + 1 and 4x³ + 3 is:

[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]

How do we multiply polynomials?

We multiply them applying the distributive property, multiplying all the terms and then combining the like terms.

In this problem, the factors are given as follows:

x³ + 2x + 1,4x³ + 3.

Hence the multiplication will be given by:

[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]

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i will mark brainlyist

The following are the distances (in miles) to the nearest airport for 12 families. 6, 7, 8, 8, 16, 19, 23, 24, 26, 27, 34, 35 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:

Answers

Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

Minimum: 6Lower quartile: 8Median: 21.Upper quartile: 27Maximum: 35Interquartile range: 19

What are the median and the quartiles of a data-set? How to find the interquartile range using it?

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

The first quartile is the median of the first half, composed by 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of the second half, composed by 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

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Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative two.

Answers

The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

What is parabola and examples?

A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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