We have been given that Layana’s house is located at [tex](2\frac{2}{3}, 7\frac{1}{3})[/tex] on a map. The store where she works is located at [tex](-1\frac{1}{3}, 7\frac{1}{3})[/tex].
We are asked to find the distance from Layana’s home to the store
We will use distance formula to solve our given problem.
Let us convert our given coordinates in improper fractions.
[tex]2\frac{2}{3}\Rightarrow \frac{8}{3}[/tex]
[tex]7\frac{1}{3}\Rightarrow \frac{22}{3}[/tex]
[tex]-1\frac{1}{3}\Rightarrow -\frac{4}{3}[/tex]
Now we will use distance formula to solve our given problem.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Upon substituting coordinates of our given point in above formula, we will get:
[tex]D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}[/tex]
[tex]D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}[/tex]
[tex]D=\sqrt{0+(\frac{8+4}{3})^2}[/tex]
[tex]D=\sqrt{(\frac{12}{3})^2}[/tex]
[tex]D=\sqrt{(4)^2}[/tex]
[tex]D=4[/tex]
Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.
Answer:
its A ^3^
Step-by-step explanation:
It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500 degrees. In a test of one type of mask, 24 of 55 were found to have their lenses pop out at 325 degrees. Construct and interpret a 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees.
Answer:
The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 55, \pi = \frac{24}{55} = 0.4364[/tex]
93% confidence level
So [tex]\alpha = 0.07[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.07}{2} = 0.965[/tex], so [tex]Z = 1.81[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 - 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.3154[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 + 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.5574[/tex]
The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).
Please answer this correctly
Answer:
easy peasy lemon squeezy
Step-by-step explanation:
Teddy has 6 lollipops and 9 cookies. Annie say for every 3 lollipops there are 2 cookies. Teddy says I don’t agree. What mistake has Annie made
Answer:
She switched her say
Step-by-step explanation:
Answer:
Annie made the mistake of either swapping the numbers or the items in her comparison.
Step-by-step explanation:
The ratio of lollipops to cookies is:
6/9
This can be simplified to:
2/3
That means that for every two lollipops, there are three cookies. Therefore Annie made the mistake of either swapping the numbers or the items in her comparison.
f(t) = t - 6
f(u + 6) =
Answer:
f(u +6) = u
Step-by-step explanation:
Put (u+6) in place of t and simplify:
f(u+6) = (u+6) -6
f(u+6) = u
Yooo I need help right now
Answer:
The answer would be 2924. 82
$100 is invested at 12% per year. If the amount is compounded annually, write the total amount after 2 years in exponential function form.
Answer:
A = $100(1.12)^2
Step-by-step explanation:
The standard formula for compound interest is given as;
A = P(1+r/n)^(nt) .....1
Where;
A = final amount/value
P = initial amount/value (principal)
r = rate yearly
n = number of times compounded yearly.
t = time of investment in years
For this case;
P = $100
t = 2years
n = 1
r = 12% = 0.12
Substituting the values, we have;
A = $100(1+0.12)^(2)
A = $100(1.12)^2
y2 – 3y + 2 = 0 solve buy factoring
Answer:
y²-3y+2=0
=> y²-(2+1)y +2=0
=> y²-2y-y+2=0
=> y(y-2)-1(y-2)=0
=> (y-2)(y-1)=0
=> y = 2 or y= 1
The Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed. The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes. At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter? What is the p-value? Use the rounded test statistic from the previous problem and round to 4 decimal places.
Answer:
We conclude that the commuting times are same in the winter.
Step-by-step explanation:
We are given that the Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed.
The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes.
Let [tex]\mu[/tex] = average commute time in winter.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 33 minutes {means that the commuting times are same in the winter}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 33 minutes {means that the commuting times are different in the winter}
The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean commute time for the month of January = 34.2
[tex]\sigma[/tex] = population standard deviation = 7.5 minutes
n = sample of drivers = 40
So, test statistics = [tex]\frac{34.2-33}{\frac{7.5}{\sqrt{40}}}[/tex]
= 1.012
The value of z test statistics is 1.012.
Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the commuting times are same in the winter.
Also, P-value of the test statistics is given by;
P-value = P(Z > 1.012) = 1 - P(Z [tex]\leq[/tex] 1.012)
= 1 - 0.84423 = 0.1558
helphelphelphelphelphelphelphelphelphelp
Answer:
Angle A equals Angle B so 6x-2=4x+48 ---> 2x=50 ---> x=25. From this we find that both Angles A and B are equal to 148 degrees. :)
A survey was taken among a group of people. The probability that a person chosen likes Italian food is 0.75, the probability that a person likes Chinese food is 0.28,
and the probability that a person likes both foods is 0.21.
Determine the probability that a person likes Italian, but not Chinese
Determine the probaility that a person likes at least one of these foods
Determine the proability that a person likes at most one of these foods -
Answer:
54% probability that a person likes Italian food, but not Chinese food.
82% probaility that a person likes at least one of these foods
79% proability that a person likes at most one of these foods
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a person likes Italian food.
B is the probability that a person likes Chinese food.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a person likes Italian food but not Chinese and [tex]A \cap B[/tex] is the probability that a person likes both Italian and Chinese food.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The probability that a person likes both foods is 0.21.
This means that [tex]A \cap B = 0.21[/tex]
The probability that a person likes Chinese food is 0.28
This means that [tex]B = 0.28[/tex]
So
[tex]B = b + (A \cap B)[/tex]
[tex]0.28 = b + 0.21[/tex]
[tex]b = 0.07[/tex]
The probability that a person likes Italian food is 0.75
This means that [tex]A = 0.75[/tex]
So
[tex]A = a + (A \cap B)[/tex]
[tex]0.75 = a + 0.21[/tex]
[tex]a = 0.54[/tex]
Determine the probability that a person likes Italian, but not Chinese
This is a.
54% probability that a person likes Italian food, but not Chinese food.
Determine the probaility that a person likes at least one of these foods
[tex]P = a + b + (A \cap B) = 0.54 + 0.07 + 0.21 = 0.82[/tex]
82% probaility that a person likes at least one of these foods
Determine the proability that a person likes at most one of these foods
Either a person likes at most one of these foods, or it likes both. The sum of the probabilities of these events is decimal 1.
0.21 probability it likes both.
Then
0.21 + p = 1
p = 0.79
79% proability that a person likes at most one of these foods
Find the volume of a right circular cone that has a height of 12.5 m and a base with a radius of 2.2 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
The volume of the cone is 63.3m³
Step-by-step explanation:
First of all to solve this problem we need to know the formula to calculate the volume of a cone
v = volume
r = radius = 2.2m
h = height = 12.5m
π = 3.14
v = 1/3 * π * r² * h
we replace with the known values
v = 1/3 * 3.14 * (2.2m)² * 12.5m
v = 1/3 * 3.14 * 4.84m² * 12.5m
v = 63.32m³
rount to the neares tenth
v = 63.32m³ = 63.3m³
The volume of the cone is 63.3m³
Answer: 63.4
Step-by-step explanation:
You round to the tenths giving you 63.4
Toxic Pollution: In the first year of a study, health officials discovered toxic pollutants in the soil surrounding a factory. The initial measurement was 65 parts per million (ppm) of pollutant. They returned to take similar measurements for several years afterward, and uncovered a disturbing trend. The pollutant levels in the soil surrounding the factory were growing exponentially, at a rate of 4.5% each year. Which exponential model predicts the amount of pollutant in the soil t years from the first measurement?
Answer:
The model for the pollutant levels in the soil t years from the first measurement is:
[tex]Y(t)=65e^{0.044}[/tex]
Step-by-step explanation:
We have a first measurement of 65 parts per million (ppm) of pollutant.
We also know that the pollutant levels were growing exponentially at a rate of 4.5% a year.
We can model this as:
[tex]Y(t)=Y_0e^{kt}[/tex]
The value of Y0 is the first measurement, that correspond to t=0.
[tex]Y_0=65[/tex]
The ratio for the pollutant levels for two consecutive years is 1+0.045=1.045. This can be expressed as the division between Y(t+1) and Y(t), and gives us this equation:
[tex]\dfrac{Y(t+1)}{Y(t)}=\dfrac{Y_0e^{k(t+1)}}{Y_0e^{kt}} =\dfrac{e^{k(t+1)}}{e^{kt}}=e^{k(t+1-t)}=e^k=1.045\\\\\\k=ln(1.045)\approx 0.044[/tex]
Then, we have the model for the pollutant levels in the soil t years from the first measurement:
[tex]Y(t)=65e^{0.044}[/tex]
The radius of a sphere is 6 units. A sphere has a radius of 6 units. Which expression represents the volume of the sphere, in cubic units?
Answer:
The volume of the sphere is 678.24 u³
V = ⁴⁄₃ * π * (6u)³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 6 units
π = 3.14
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * 3.14 * (6u)³
V = 4.187 * 216 u³
V = 678.24 u³
The volume of the sphere is 678.24 u³
Consider the system of linear equations. 7 x + 16 y = negative 2. 9 x minus 4 y = 22. To use the linear combination method and addition to eliminate the y-terms, by which number should the second equation be multiplied? –4 Negative one-fourth One-fourth 4
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Raul is y years old. Kayla is 6 years older than raul and isaac is 4 years younger than raul what is kayla's age?
Answer:
9
Step-by-step explanation:
An author argued that more basketball players have birthdates in the months immediately following July 31, because that was the age cutoff date for nonschool basketball leagues. Here is a sample of frequency counts of months of birthdates of randomly selected professional basketball players starting with January: 390, 392, 360, 318, 344, 330, 322, 496, 486, 486, 381, 331 . Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency? Do the sample values appear to support the author's claim?
Answer:
There is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
Step-by-step explanation:
In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum{\frac{(O-E)^{2}}{E}}[/tex]
The values are computed in the table.
The test statistic value is [tex]\chi^{2}=128.12[/tex].
The degrees of freedom of the test is:
n - 1 = 12 - 1 = 11
Compute the p-value of the test as follows:
p-value < 0.00001
*Use a Chi-square table.
p-value < 0.00001 < α = 0.05.
So, the null hypothesis will be rejected at any significance level.
Thus, there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
Final answer:
To test the claim that professional basketball players are born in different months with the same frequency, a chi-square test for goodness of fit can be used. Calculations involve comparing the actual birthdate frequencies of the players against the expected frequencies if the distribution were uniform. A statistically significant result would support the author's claim, while a non-significant result would not.
Explanation:
Chi-Square Test for Uniform Distribution
To determine if there is sufficient evidence to support the author's claim that professional basketball players are born in different months with the same frequency, we can perform a chi-square test for goodness of fit. Given the frequency counts of the birthdates of professional basketball players for each month, we will compare them to the expected frequencies if births were uniformly distributed throughout the year.
Steps to Perform the Test
Firstly, calculate the total number of players in the sample by summing up the frequency counts for each month.
Determine the expected frequency for each month, which would be the total number of players divided by 12, assuming a uniform distribution.
Calculate the chi-square statistic using the formula: χ² = ∑((observed - expected)² / expected), where 'observed' is the frequency count for each month, and 'expected' is the expected frequency.
Compare the calculated chi-square value with the critical value from the chi-square distribution table with 11 degrees of freedom (since there are 12 months - 1) and a significance level of 0.05.
If the chi-square value is greater than the critical value, reject the null hypothesis (that the birth months are uniformly distributed), which supports the author's claim. Otherwise, do not reject the null hypothesis.
Interpretation
By performing the calculations, if the chi-square test statistic is greater than the critical value, it suggests that there is a statistically significant difference in the distribution of birth months among professional basketball players. This would support the author's claim that there may be more players born in the months immediately following July 31, which is the age cutoff date for nonschool basketball leagues. If the test statistic is not greater than the critical value, there is not enough evidence to support the claim.
A car travels at an average speed of 52 miles per hour. How many miles does it travel in 5 hours and 45 minutes?
Answer:
299
Step-by-step explanation:
On average, it travels 52 miles in each hour. In 5 3/4 hours, it travels 5 3/4 times 52 miles.
(5 3/4)(52 miles) = 299 miles
It travels 299 miles in the given time.
Answer:
The car will travel 195 miles.
Step-by-step explanation:
(3.75 hrs)(52 mph)=195 miles
What is the following quotient 3 square root 8 4 square root 6
Answer: √3/2
Step-by-step explanation: Ok...so it would look like this:
(3√8)/(4√6)
I hope this helps!
You work for a company in the marketing department. Your manager has tasked you with forecasting sales by month for the next year. You notice that over the past 12 months sales have consistently gone up in a linear fashion, so you decide to run a regression the company's sales history. You find that the regression equation for the data is (sales) = 128.329*(time) + 115.362. In August (time = 8) you see the actual sales quantity was 322.492. The residual is -819.502. Interpret this residual in terms of the problem.
01) The month is 819.502 months less than what we would expect.
02) The month is 819.502 months larger than what we would expect.
03) The sales is 819.502 units greater than what we would expect.
04) The sales is 819.502 units less than what we would expect.
05) The sales is 322.492 units less than what we would expect.
3Answer:
Step-by-step explanation:
PLEASE IM BEING TIMED
Answer:
A
Step-by-step explanation:
First you use the equation [tex]2(\pi r^{2})[/tex] to find the area of the circles combined and you find the radius by diving the height by 2(getting 5)
Then you find the area of the squares with the circles(10 x 20= 200)
Finally you subtract the area of both circles and the total area. (200-157=43)
Consider the recursively defined set S: Basis Step: The unit circle is in S. Recursive Step: if x is in S, then x with a line through any diameter is in S. (a) (4 points) Prove that: is in S. (b) ( 6 points) For an element x ∈ S, define V (x) be the number of vertices (i.e. the number of intersections of lines and arcs and lines with lines), let E(x) to be the number of edges (line segments or arcs between vertices), and let F(x) be the number of faces. Prove that for any x ∈ S that F + V = E + 1. (Please use structural induction.)
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation to the question
What is the complete factorization of 8x^2 - 8x + 2?
Step-by-step explanation:
8x² − 8x + 2
2 (4x² − 4x + 1)
2 (2x − 1)²
Which is similar to this quadrilateral?
Answer:
D
Step-by-step explanation:
D has the most similarities than others
The option B is correct.
Definition of similarity :Two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same and two adjacent sides have equal ratios.The option B quadrilateral is similar to the given quadrilateral.
Because the three corresponding angles are the same.
Therefore, option B is correct.
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The distance between sides of a polygon is always the same
Answer:
yes
Step-by-step explanation:
By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides.
Since it is true that the distance between sides of a polygon are always the same.
What is a polygon?A polygon is defined as a closed figure made up of three or more line segments connected end to end
For a regular polygon of any number of sides, then the sum of its exterior angle is 360° .
Exterior angle is an measure of rotation between one extended side of the polygon with its adjacent side which is not extended. Also, regular having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.
When a polygon is four sided (a quadrilateral), the sum of its angles is 360°
Based on the definition, all sides are the same length, thus the perimeter is simply the length of a side times the number of sides.
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You are thinking about the things that can go wrong on your trip home over the Thanksgiving break. You have booked a flight with US-Scareways. You know that in 28 percent of the cases the company has canceled the flight you were on. Should such a thing occur, there would be no other air travel option home for you. As a backup, your friend Walter has offered you a ride back. However, you know that Walter only has a seat in his car for you with 84 percent probability. What is the Probability of you making it home for the holidays
Answer:
0.9552
Step-by-step explanation:
Probability of making home can be made by either of the options :-
Prob (Reach through flight) : 1 - prob (flight not cancelled) = 1 - 0.28 = 0.72Prob (Reach through car) : prob (flight cancelled & car seat is available) = 0.28 x 0.84 = 0.2352So, probability of making out at home : Reach through flight or car = 0.72 + 0.2352 = 9.9552
Final answer:
The probability of making it home for the holidays can be calculated using conditional probability. The probability of the flight being canceled is 28 percent, and the probability of Walter having a seat in his car is 84 percent. The probability of making it home is approximately 60.48 percent.
Explanation:
The probability of making it home for the holidays can be calculated using the concept of conditional probability. The probability of the flight being canceled is given as 28 percent, which means there is a 72 percent chance that the flight is not canceled. The probability of Walter having a seat in his car is given as 84 percent. To calculate the probability of making it home, we need to calculate the probability of both events happening.
The probability of the flight not being canceled is 72 percent (0.72) and the probability of Walter having a seat is 84 percent (0.84). To find the probability of both events happening, we multiply the probabilities: 0.72 * 0.84 = 0.6048 or approximately 60.48 percent. So, there is a 60.48 percent probability of making it home for the holidays.
QUESTION 1 of 10: Which of the following is NOT a true statement?
a) Knowing the diferent food groups and how many servings from each group will allow you to have a balanced diet.
b) All work and no relaxation can compromise your health.
C) Technology benefits people by allowing them to avoid sore muscles.
d) Lack of sleep leads to increased risk for motor vehicle accidents.
Answer:
c
Step-by-step explanation:
cuzz im right
Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Select two options
The vertex form of the function is f(x) = (x - 2)2 + 2.
The vertex of the function is (-3, -13).
The axis of symmetry for the function is x = 3.
The graph increases over the interval (-3,
).
The function does not cross the x-axis.
Answer:
2 and 4
Step-by-step explanation:
A function assigns the values. The statements that are true about the given function are B and D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To know the correct statements about the graph of the function f(x)=6x-4+x², we need to plot the graph, as shown below.
A.) The vertex form of the function is f(x)=(x-2)²+2.
To know if the vertex form of the function is f(x)=(x-2)²+2, solve the equation and check if it is of the form f(x)=6x-4+x².
[tex]f(x)=(x-2)^2+2\\\\ f(x)=x^2+4-4x+2\\\\f(x) = x^2-4x+6[/tex]
Since the two functions are not equal this is not the vertex form of the function is f(x)=6x-4+x².
B.) The vertex of the function is (-3, -13).
As can be seen in the image below, the vertex of the function lies at (-3,-13.) Therefore, the statement is true.
C.) The axis of symmetry for the function is x = 3.
As the vertex is at -3, therefore, the function symmetry will be about x=-3.
Hence, the given statement is false.
D.) The graph increases over the interval (-3).
The given statement is true since the graph will be showing a positive slope in the interval (-3, +∞).
E.) The function does not cross the x-axis.
It can be observed that the function intersects the x-axis exactly at two points, therefore, the given statement is false.
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Does anybody know these two questions?!
Answer:
Both are true statements
Step-by-step explanation:
By definition of an angle, an angle is a union of two rays at a common endpoint and lines can contain rays.
A full circle measures 360 degrees.
Answer:
Question7:true
Question8:true
Step-by-step explanation:
Question 7: an angle is made when two lines or rays come together
Question 8:an angle that has 360° is a circle
Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ____________.
Answer:
The null hypothesis is H0; u1 - u2 = 0
The mean age of each audience is the same.
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
Therefore, for the case above;
Let u1 represent the mean age of audience for American idol and
u2 represent the mean age of audience for 60 minutes.
The null hypothesis is H0; u1 - u2 = 0
The mean age of each audience is the same.
which function does this graph represent
A. f(x) = 3(x + 1)^2 + 2
B. f(x) = -3(x + 1)^2 + 2
C. f(x) = -3(x + 1)^2 - 2
D. f(x) = 3(x - 1)^2 + 2
The equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.
What is parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Here, general equation of parabola in downward direction is
(y-y₁) = -4a(x-x₁)²
vertex of parabola (-1, 2)
(y-2) = -4a(x-(-1))²
(y - 2) = -4a(x + 1)²
put the value of x = 0 and y = -1
so we get, a = 3/4
put in equation of parabola
( y - 2 ) = -3 ( x + 1 ) ²
y = -3 (x + 1)² + 2
f(x) = -3 (x + 1)² + 2
Thus, the equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.
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