Which parabola below has a maximum value?
a. y = 0.1x2 - 3x
b. y = 4x2 + 24x +23
c. y = 2x - 3x2
d. y = x2 + 2x + 20
In the given parabola equations, the third equation [tex]y = 2x - 3x^{2}[/tex] has a maximum value.
What is the Maximum parabola?
If a parabola opens up, it has the lowest point, and if it opens down, it has the highest point. For a parabola to have a maximum value, it must be the case that the parabola opens down. Algebraically, this means that the leading coefficient in the equation of a parabola is negative (a < 0).
We have,
[tex]y = 0.1x^{2} - 3x\\\\y = 4x^{2} + 24x +23\\\\y = 2x - 3x^{2}\\\\y = x^{2} + 2x + 20[/tex]
For a parabola to have a maximum value, the parabola must open downward. Algebraically, this means that the leading coefficient in a parabola equation is negative (a < 0).
By Simplifying the third equation we get its leading coefficient is negative (a < 0).
[tex]y = -3x^{2} + 2x[/tex]
Hence in the given parabola equations, the third equation has a maximum value.
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can the sum X to the power of two plus X to the power of three be written in simpler form? explain.
The sum X to the power of two plus X to the power of three be written in simpler form is X² + X³.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Based on the information given, this will be illustrated as X² + X³. In this case, it illustrate the addition of exponents.
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White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 7:3
The ratio of the number of white circles to the number of white squares is 2:7
The ratio of the number of black circles to the number of black squares is 1:2
Work out what fraction of all the shapes are circles.
Give your answer as a fraction in its simplest form.
(Hint: Fractions can be written in the form a/b. eg [tex]\frac{5}{28}[/tex] would be written as 5/28)
The fraction of all the circles in the shapes is 23/90
How to calculate the fraction of all the shapes are circles?Given that the:
Ratio of the number of white shapes to the number of black shapes is 7:3
Ratio of the number of white circles to the number of white squares is 2:7
Ratio of the number of black circles to the number of black squares is 1:2
Total share for both white and black shape = 7+3 = 10
share for white shape = 7/10 and share for black shape = 3/10
Total share for white circles and white squares = 2+7 = 9
share for white circles = 2/9 and share for white squares = 7/9
Total share for black circles and black squares = 1+2 =3
share for black circles = 1/3 and share for black squares = 2/3
White circles will take 2/9 of white colors i.e. 2/9 x 7/10 = 14/90 = 7/45
Black circles will take 1/3 of black colors i.e. 1/3 x 3/10 = 3/30 = 1/10
Fraction of circles = 7/45 + 1/10
= 14+9/ 90
= 23/90
Therefore, the fraction of all the shapes that are circles is 23/90
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Gerardo and his two friends order a pizza and decide to split the cost evenly. Each person ordered a drink for $1.50. How much was the pizza if each person paid $8?
19.50 cost of pizza
Step-by-step explanation:
$8.00-$1.50 = $6.50 × 3 =19.50
suppose a sample of thirty 25- to 34-year-olds showed a sample mean of 118.4 texts per day. assume a population standard deviation of 33.17 texts per day. compute the p-value. (round your answer to four decimal places.) p-value
The p-value of the distribution of population standard deviation of 33.17 texts per day is 0.9435
The test statistic's "p-value" measures how likely it is that future results will be at least as extreme as the one your sample yielded. You must understand that the null hypothesis is the underlying presumption to compute this probability.
The parameters are as follows:
The sample mean ([tex]\bar x[/tex]) = 118.4
The population standard deviation ([tex]\sigma[/tex]) = 33.17
The sample size (n) = 30
Calculate the z-score first.
[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }[/tex]
according to the entire question, x = 128
So, we have:
[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{\sqrt{30} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{5.477 } } }\\\\z = \bold{ \frac{9.6}{ 6.056} }\\\\z = 1.5852[/tex]
As determined by the z table of probability, p = 0.9435395
or p = 0.9435 (approx.)
Consequently, the distribution's p-value is 0.9435.
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Ms. Lewinsky’s math class has k students. If p students earned a C or better on the last test, what fraction of the class did NOT eat a C or better on the last test?
Answer:
its "a" your welocome
Step-by-step explanation:
i did the test
A small publishing company is planning to publish a new book. Let C be the total os of publishing the book(in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 300 copies of the book. Suppose that c=20N+500 gives C as function of N during the first printing.
The set of vale is the same for both.
The cost of publishing the 300 copies of the book is $6500.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a small publishing company is planning to publish a new book. Let C be the total os of publishing the book(in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 300 copies of the book. Suppose that c=20N+500 gives C as a function of N during the first printing.
The cost of 300 copies will be calculated as,
c=20N+500
c = ( 20 x 300 ) + 500
c = 6000 + 500
c = 6500
Therefore, the cost of publishing the 300 copies of the book is $6500.
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b. Which of these products has the same value as 4(12)? Select all that apply.
A.
8(6)
B.
76
C.
316
D.
12(4)
E.
124
Answer:
A and D
Step-by-step explanation:
8(6) means 8x6 so that's 48
and 12(4) is the same as 4(12) so that should be simple enough
Classify the following inequalities into the given categories. Drag each inequality into the appropriate category. Strict inequality Nonstick inequality
3x-2<1
3x-> 1
3x-2>1
3x-2<1
All the inequality given are all non strict inequalities
Inequality classification
3x - 2 < 1 non strict inequality
3x - > 1 non strict inequality
3x - 2 > 1 non strict inequality
3x - 2 < 1 non strict inequality
What is inequality ?Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe strict inequality are those inequality that the equation fails when equality sign is used to represent the relationship of the left and right hand side of an equation.. The inequality sign used here is only less than or greater than
The non strict inequality maintains the balance between both sides of the equation whether the equality is used or not
None of the given expression has the "less than or equal to" OR "greater than or equal to" signs hence they are all strict inequality
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find the value of x in each case
the sum of emma's age and her sister's age is 48 years. emma's age is 6 years less than twice her sister's age. what is emma's age, and what is her sister's age?
Zachary is applying biomechanics to develop a specialized bat for a professional player. What does he compar
the hitter to?
Oa machine
O a computerized model
O another professional player
O a 3-D diagram
Answer:
Another Professional Player
a surgeon developed a new procedure for knee replacement surgery. to study its effectiveness, they recruit patients who need knee replacement surgery and are willing to participate in a blind study. the surgeon randomly assigns each volunteer to receive either the new procedure or the standard procedure. after the surgeon performs the procedure, they monitor each patient to see if one group has better results than the other. what does it mean for this experiment to be blind?
Answer: The volunteers are unaware of which surgery they receive.
Step-by-step explanation:
Please help with the unfilled spots! :)
The value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex],according to the question.
What do you mean by XY coordinates?
The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.
According to the data in the given question,
We have:
The coordinates of points A are (-9,-6).
The coordinates of points W are (-1,-12).
In this question,
[tex](x_{1},y_{1})= (-9,-6)[/tex]
[tex](x_{2},y_{2})= (-1,-12)[/tex]
Therefore, the value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex].
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shopper needs 48 hot dogs. The store sells identical hot dogs in 2 differently sized packages. They sell a six-pack of hot dogs for $2.10, and an eight-pack of hot dogs for $3.12.
The pack of hot dogs that the shopper should buy that would be cheaper is six - pack of hot dogs
How to find the pack to be bought?If the shopper decided to buy the six-pack of hot dogs for $2.10, their total cost to be able to get 48 hot dogs would be:
= Cost per six pack of hot dogs x ( Number of hot dogs needed / Number of hot dogs in pack)
=2.10 x (48 / 6)
= 2.10 x 8
= $16.80
The cost if the shopper wants the eight pack is:
= 3.12 x (48 / 8)
= $18.72
The shopper should pick the six - pack of hot dogs because it is cheaper.
The rest of the question is:
Which option would be cheaper to the shopper?
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The manager of a movie theater compared ticket
sales for two movies showing on the same night.
For the first movie, 150 adult tickets and
100 child tickets were sold for $3,087.50 in total
ticket sales. For the second movie, 200 adult
tickets and 150 child tickets were sold for
$4,287.50 in total ticket sales. What was the price
of each adult and each child ticket?
Answer:
adult: $13.75child: $10.25Step-by-step explanation:
You have two revenue relations and want the price of each adult and child ticket. 150 adult and 100 child tickets sold for $3087.50; 200 adult and 150 child tickets sold for $4287.50.
EquationsEach of the revenue relations can be formulated as an equation. If x and y represent the price of each adult and child ticket, respectively, then ...
150x +100y = 3087.50
200x +150y = 4287.50
SolutionThe solution can be found many ways. A graphing calculator (first attachment) shows the solution to be ...
adult price: $13.75child price: $10.25The calculator function that reduces a matrix to row-echelon form can be used on the augmented matrix of coefficients. That, too, gives the solution about as quickly as you can enter the coefficients. This is shown in the second attachment.
Subtracting twice the second equation from 3 times the first will eliminate the y-variable:
3(150x +100y) -2(200x +150y) = 3(3087.50) -2(4287.50)
50x = 687.50
x = 13.75 . . . . . . divide by 50
From the second equation, ...
y = (4287.50 -200(13.75))/150 = 1537.50/150
y = 10.25
Joe and Chris share a locker at school. if they each have 8 classes and each class has 2 books, how many books are in the locker. Please show the work! :)
Answer:
32 books
Step-by-step explanation:
Well if each have 8 classes and 2 books per class then to get the total of books you'd multiply 8x2 and you get 16 for one alone. Since its two people sharing a single locker than add 16 with another 16 and you get 32!
sorry I can't physically show the work but writing down a 8x2 on the side and then adding 16 to that answer should show it off! :]
Ms.emlyn buys a hat and gloves with a coupon for 30% off her entire purchase. the gloves cost $35 before the discount. her bill before tax is $44.80.write an equation to find the original cost of the hat.
The equation to find the original cost of hat is
44.80 = (x + 35) - (x+35)× 10/3
In the given question we have,
Ms. emlyn buys a hat and gloves with coupon for 30% off her entire purchase.
discount on total purchase = 30%
cost of gloves before discount = $35
let the cost of hat be $x before discount . The bill paid by Ms emlyn after discount but without tax = $44.80
total cost ( hat+gloves) before discount= $(x+35)
Now, after sum up all information we get,
$(x+35) - 30%discount on $(x+35) = $44.80
=> x+35 - (x+35)100/30 = 44.80
=> x+35 - (x+35)10/3= 44.80
which is required equation for original cost of hat.
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The total cost of a one-year membership at a gym is £141. This is made
up of a single £57 sign-up fee and equal-sized monthly payments for the
whole year.
How much is each monthly payment?
Give your answer in pounds.
Answer: 7£
Step-by-step explanation:
1. Firstly, we need to subtract the single sign up fee from the total cost. This would be 141-57 =84 pounds
2. We know that you pay a regular amount every month, so therefore we can divide 84 by 12 as there are 12 months in a year.
3. 84/12 = 7. Thus, the answer is 7 pounds a month.
Answer:
£7
Step-by-step explanation:
Given information:
£141 = Total cost of one-year gym membership.£57 = sign-up fee (included in the annual fee).To find the cost of the monthly payments, find the difference between the total cost and the sign-up fee, then divide the result by 12 (as there are 12 months in one year).
The difference between the total cost and the sign-up fee is:
[tex]\implies 141-57=84[/tex]
Therefore, the cost of each monthly payment is:
[tex]\implies \textsf{Monthly fee}=\dfrac{84}{12}=7[/tex]
2. Beth and Reena opened Basic Savings accounts on the same day. Reena's initial deposit was twice as much as Beth's. After 5 years, their combined interest earned was $21.00. What was the amount of Reena's initial deposit?
Answer:
Step-by-step explanation:
A=P(1+r/n)^nt
Let the Beth deposite is x.Here r and n will be 1.
A=x(1+1/1)^5
Similarly
B=2x(1+1/n)^nt
B=2x(1+1/1)^5
There combined interest is:
A+B=x(1+1/1)^5+2x(1+1/1)^5
21=32x+64x
21=96x
x=21/96 is the beth deposite.
2x=2*21/96 is the Reena deposite
help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
h = 289 feet
Step-by-step explanation:
Comment
You need two givens to use in the formula to solve for the third.
Formula
v = sqrt(2*g*h)
Givens
V = 136 ft/s
g = 32 ft/s^2
h = ?
Solution
v = sqrt(2*g*h) Put the givens into the formula.
136 = sqrt(2* 32 * h) Square both sides
136^2 = sqrt(2*32*h)^2 Expand
18496 = 64* h Divide by 64
18496/64 = 64*h/64
289 feet = h
So the object must fall 289 feet before it reaches 136 m/s
5/3=?x1/3
help please ASAP
The value of x is 5 for the given equation 5/3 = x/3.
What do we mean by equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.So, the equation is:
5/3 = x/3Now, solve for x as follows:
5/3 = x/33x = 5 × 3 (Cros multiply)3x = 15x = 15/3x = 5Therefore, the value of x is 5 for the given equation 5/3 = x/3.
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Correct question:
Solve for x. 5/3= x/3
the table below gives the annual sales (in millions) of a product. year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 273 327 369 399 417 423 417 399 369 what was the average rate of change of annual sales a) between 2001 and 2002 millions of dollars/year b) between 2001 and 2006 millions of dollars/year
Main answer:
a) 18 millions of dollars/year
b) 6 millions of dollars/year
Step-by-step explanation:
a) the average rate of change of annual sales between 2001 and 2002 millions of dollars/year
Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)
= (417 - 399) / (2001 - 2002)
= 18 / 1
= 18 millions of dollars/year
b) the average rate of change of annual sales between 2001 and 2006 millions of dollars/year
Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)
= (369 - 399) / (2006 - 2001)
= 30 / 5
= 6 millions of dollars/year
The average rate of change of annual sales between 2001 and 2002 is 18 millions of dollars/year , between 2001 and 2006 is 6 millions of dollars/year
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According to flightstats com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 20 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment (b) Determine the values of n and p. (c) Find and interpret the probability that exactly 12 flights are on time. (d) Find and interpret the probability that fewer than 12 flights are on time. (e) Find and interpret the probability that at least 12 flights are on time. (f) Find and interpret the probability that between 10 and 12 flights, inclusive, are on time.
As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
The value of p=0.8 and n=20
The probability that exactly 12 flights are on time = 0.1772
The probability that exactly fewer than 12 flights are on time = 0.1049
The probability that at least 12 flights are on time = 0.8951
The probability that between 10 and 12 flights, are on time = 0.1795
(a) Binomial probability is the probability of exactly 'k' successes on 'n' repeated trials in an experiment which has two possible outcomes.
As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
(b) As, the probability of success on an individual trial is p and here success means the flight is on-time so the value of p be,
p = 80% = 0.8
As, we made 20 trials and n is the total number of trials then,
the value of n be,
n = 20
(c) Now, if the probability of success on an individual trial is p ,
Then the binomial probability is C(n,x)⋅p^x⋅(1−p)^(n−x)
The probability that exactly 12 flights are on time, be
P(X=12) = C(20,12)⋅(0.8)^12⋅(1−0.8)^(20-12)
P(X=12) = C(20,12)⋅(0.8)^12⋅(0.2)^(8)
P(X=12) = 10,07,760×0.0687×0.00000256
P(X=12) = 0.1772
(d) Now, the probability that exactly fewer than 12 flights are on time, be
P(X<12) = 1 - P(X>12)
So, P(X>12) = P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)
So, P(X>12) = 0.0545 + 0.0364 + 0.1746 + 0.2182 + 0.2054 + 0.1369 + 0.0576 + 0.0115
P(X>12) = 0.8951
P(X<12) = 1 - 0.8951
P(X<12) = 0.1049
(e) Now, the probability that at least 12 flights are on time, be
P(X>12)=0.8951
(f) The probability that between 10 and 12 flights, are on time, be
P(X=10)+P(X=11)+P(X=12) = 0.0020 + 0.0003 + 0.1772
P(X=10)+P(X=11)+P(X=12) = 0.1795
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couple has 5 kids, all sons. if they have a sixth kid, what is the probability that the sixth kid will be a son?
What is the third term of the sequence 20 - n²
A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
As per the given sequence, 20 - n²
The 20 - n² represents the nth term of the sequence.
Thus a(n) = 20 - n²
For the third term n = 3
a(3) = 20 - (3)²
a(3) = 20 - 9 = 11
Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".
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why is it important to create a budget even if you don’t get a lot of money or if you have an irregular income?
Answer:
it is important because this will be helpful for your incomes, tax, bills etc. This also will plan for other things that you might pay like savings.
Step-by-step explanation:
PLEASE HELP MEEE!!!!!!!!!
Each function operation should be matched with what it is equivalent to as follows:
f(x) + g(x) = -2x² + x + 6.
g(x) - f(x) = -2x² - 5x + 2.
f(x) · g(x) = -6x³ - 10x² + 8x + 8.
h(x) - f(x) = 3x² - 7x - 2
f(x) · h(x) = 9x³ - 6x² - 8x.
f(x) + g(x) + h(x) = x² - 3x + 6.
How to determine the solutions of the given function?In order to determine the solutions of the given function, we would have to evaluate each of the function based on the required mathematical operations as follows.
From the information provided, we have the following functions:
f(x) = 3x + 2
g(x) = -2x² - 2x + 4
h(x) = 3x² - 4x
f(x) + g(x) = 3x + 2 + (-2x² - 2x + 4)
f(x) + g(x) = 3x + 2 - 2x² - 2x + 4
Next, we would rearrange the function by collecting like terms as follows:
f(x) + g(x) = -2x² + (3x - 2x) + (2 + 4)
f(x) + g(x) = -2x² + x + 6 (solution).
g(x) - f(x) = -2x² - 2x + 4 - (3x + 2)
Opening the bracket, we have:
g(x) - f(x) = -2x² - 2x + 4 - 3x - 2
Next, we would rearrange the function by collecting like terms as follows:
g(x) - f(x) = -2x² + (-2x - 3x) + (4 - 2)
g(x) - f(x) = -2x² - 5x + 2 (solution).
f(x) · g(x) = (3x + 2) × (-2x² - 2x + 4)
Opening the bracket, we have:
f(x) · g(x) = -6x³ - 6x² + 12x - 4x² - 4x + 8
Next, we would rearrange the function by collecting like terms as follows:
f(x) · g(x) = -6x³ + (-6x² - 4x²) + (12x - 4x) + 8
f(x) · g(x) = -6x³ - 10x² + 8x + 8 (solution).
h(x) - f(x) = 3x² - 4x - (3x + 2)
h(x) - f(x) = 3x² - 4x - 3x - 2
h(x) - f(x) = 3x² - 7x - 2 (solution).
f(x) · h(x) = (3x + 2) × (3x² - 4x)
f(x) · h(x) = 9x³ - 12x² + 6x² - 8x
f(x) · h(x) = 9x³ - 6x² - 8x (solution).
f(x) + g(x) + h(x) = 3x + 2 + (-2x² - 2x + 4) + (3x² - 4x)
f(x) + g(x) + h(x) = -2x² + x + 6 + 3x² - 4x
f(x) + g(x) + h(x) = x² - 3x + 6 (solution).
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A corporation earned a profit of $2. 5 x 10 to the 4th power for 1 x 10 to the 3rd power days in a row. What was the corporation's total profit during this time period?
Answer in both scientific notation and standard form
The overall profit of the corporation as during time period is $ 2.5 x 10⁷
Define the term scientific notation?Scientific Notation (also known as Standard Form) is a process of presenting numbers in a concise manner. A number expressed in Scientific Notation is a number between 1 and less than 10, scaled by such a power of ten. Move this decimal point such that there one digit (that cannot be zero) before it.As the question expressed-
Earned profit - $2. 5 x 10 to the 4th power
In scientific notation - $2. 5 x 10⁴
Number of days - 1 x 10 to the 3rd power
In scientific notation - 1.0 x 10³
Total profit = Earned profit x Number of days
Total profit = $2. 5 x 10⁴ x 1.0 x 10³
Total profit = $ 2.5 x 10⁷
Thus, the overall profit of the corporation as during time period is $ 2.5 x 10⁷.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola from the vertex is f(x) = 7(x - 3)² + 5
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 7x²
Also, we have
Vertex = (3, 5)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 3)² + 5
This also means that
f(x) = 7(x - 3)² + 5
The 7 is gotten from f(x) = 7x²
Hence, the equation of the parabola is f(x) = 7(x - 3)² + 5
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