A quadratic function should have an exponent of 2, a parabola ending its life by going down should have a leading coefficient sign of negative, and either y = x^2 or y = -x^2 can be a valid equation for a quadratic function, with the choice depending on the direction of the desired parabola.
1. The quadratic should have an exponent of 2, as a quadratic is a polynomial of degree 2.
2. A parabola ending its life by going down should have a leading coefficient sign of negative, as this indicates that the quadratic term has a negative coefficient and the parabola opens downwards.
3. Both equations, y = x^2 and y = -x^2, are valid equations for a quadratic function. The main difference between them is the direction in which the parabola opens. The equation y = x^2 represents a parabola that opens upwards, while y = -x^2 represents a parabola that opens downwards. The choice of which equation to use depends on the specific context and the direction of the desired parabola.
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What is the area of a triangle with vertices at (5,0), (-3,1) and (2,6)?
6 units squared
54 units squared
22. 5 units squared
36. 5 units squared
Answer:
To find the area of a triangle given its vertices, we can use the formula:
Area = 1/2 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|
where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices.
Using this formula, we can calculate the area of the triangle with vertices at (5,0), (-3,1), and (2,6) as follows:
Area = 1/2 * |(5*(1-6) + (-3)(6-0) + 2(0-1))|
= 1/2 * |-25 - 18 - 2|
= 1/2 * |-45|
= 22.5
Therefore, the area of the triangle is 22.5 units squared. So the answer is option C: 22.5 units squared.
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Your friends, Fernando and Amelia, each own a video game designer company. They both want you to join their company. You currently have a part-time job making $8. 00 per hour. Fernando offers to pay you $15 per hour for the first month and then increase your hourly rate by $1. 00 each month. Amelia says she will start your pay at $8. 00 per hour but she will increase your hourly rate by 10% each month. In order to make the best decision, you decide to use the mathematics to choose the best offer based on the best hourly wage per month.
Write the equations to represent Fernando’s job offer and Amelia’s job offer. Let x = number of months, y = hourly wage.
Under what time period would you accept Fernando’s offer? Use mathematics to support your reasoning.
Under what time period would you prefer Amelia’s offer? Use mathematics to support your reasoning.
Now that we have looked at the different figures for Fernando and Amelia, which job would you take for the long run? Use mathematics to justify your answer
Answer:
The equation to represent Fernando's job offer is:
y = 15 + x
Where y is the hourly wage and x is the number of months worked.
The equation to represent Amelia's job offer is:
y = 8(1 + 0.1)^x
Where y is the hourly wage and x is the number of months worked.
To determine the time period for which Fernando's offer is better, we need to find the point where his hourly wage is greater than Amelia's. We can set the two equations equal to each other and solve for x:
15 + x = 8(1 + 0.1)^x
15 + x = 8(1.1)^x
x ≈ 20.44
Therefore, Fernando's offer is better for any time period greater than 20.44 months.
To determine the time period for which Amelia's offer is better, we need to find the point where her hourly wage is greater than Fernando's. We can set the two equations equal to each other and solve for x:
8(1 + 0.1)^x = 15 + x
8(1.1)^x = 15 + x
x ≈ 14.45
Therefore, Amelia's offer is better for any time period less than 14.45 months.
For the long run, we need to determine which offer has a higher hourly wage after a certain number of months. We can compare the two equations by finding their limits as x approaches infinity:
lim (y = 15 + x) as x → ∞ = ∞
lim (y = 8(1 + 0.1)^x) as x → ∞ = ∞
Therefore, both offers have the same long-term hourly wage of infinity. However, Fernando's offer has a faster rate of increase, so it may be more beneficial in the long run.
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Mario had 40 shares of stock that each lost $75 during the half of the year. He also had 24 shares of a different stock that gained $50 each. What was his net change during this time period on these stocks?
The net change in the stock is $1800
How to calculate the net change ?Mario has 40 shares of stick that each lost $75 during half of the year
He also had 24 shares of a different stock that gained $50
The net change can be calculated as follows
-40 × 75
= -3000
= 24 × 50
= 1200
Net change
-3000 + 1200
= -1800
Hence the net change in the stocks is $1800
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Solve for a.
5
a = [?]
3
a
evaluate the square root
before entering your
answer.
pythagorean theorem: a2 + b2 = c2
By evaluating square root and using Pythagorean Theorem the value of a is a= 3.33 (rounded to two decimal places)
The given expression is 5/3, which can be simplified as follows:
a = 5/3
To evaluate the square root of a, we can rewrite it in terms of exponents:
a = (5/3)¹/₂
Using a calculator, we get:
a ≈ 1.83
Next, we can use the Pythagorean Theorem to find the value of c, given that a = 3.33 and b = 4.66:
a² + b² = c²
(3.33)² + (4.66)² = c²
11.0889 + 21.7156 = c²
32.8045 = c²
c ≈ 5.72
Therefore, the final answer is a = 3.33 and c ≈ 5.72.
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A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
The correct interpretation of the 95% confidence level is that if we were to repeat this sampling process multiple times and construct confidence intervals in the same way, about 95% of the intervals would contain the true mean number of suitable apples produced per tree.
In other words, we are 95% confident that the true mean number of suitable apples produced per tree is between 375 and 520 based on this particular sample of 40 trees. However, we cannot say with certainty that the true mean falls within this interval, nor can we say that it falls outside of this interval with 95% confidence.
It's important to note that the confidence level refers to the long-run behavior of the method of constructing confidence intervals, rather than the probability that the true mean falls within the specific interval calculated from this one sample.
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Auto Loans ~ George works for a credit union that serves a large, urban area. For his annual report, he wants to estimate the mean interest rate for 60-month fixed-rate auto loans at lending institutions (banks, credit unions, auto dealers, etc. ) in his area. George selects a random sample of 12 lending institutions and obtains the following rates:
The estimated mean interest rate for 60-month fixed-rate auto loans at lending institutions in the urban area is 3.59% (the calculated mean from the given data).
To calculate the estimated mean interest rate, we need to find the average of the interest rates provided by the 12 lending institutions. The given data is as follows:
3.25%, 3.50%, 3.75%, 3.25%, 3.80%, 3.90%, 3.95%, 3.75%, 3.40%, 3.50%, 3.60%, 3.65%
The mean is calculated by adding up all the interest rates and then dividing by the total number of rates. Therefore,
Mean = (3.25 + 3.50 + 3.75 + 3.25 + 3.80 + 3.90 + 3.95 + 3.75 + 3.40 + 3.50 + 3.60 + 3.65)/12
Mean = 3.59%
Hence, the estimated mean interest rate for 60-month fixed-rate auto loans at lending institutions in the urban area is 3.59%.
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The OLS estimator is derived by: Group of answer choices connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi making sure that the standard error of the regression equals the standard error of the slope estimator. Minimizing the sum of absolute residuals. Minimizing the sum of squared residuals
Minimizing the sum of squared residuals.
How is the OLS estimator derived?The OLS (Ordinary Least Squares) estimator is derived by minimizing the sum of squared residuals. This method aims to find the line of best fit that minimizes the vertical distance between the observed data points (Yi) and the predicted values on the regression line. The residuals represent the differences between the observed values and the predicted values.
By minimizing the sum of squared residuals, the OLS estimator ensures that the line fits the data as closely as possible. This approach is based on the principle of least squares, which seeks to find the parameters that minimize the overall discrepancy between the observed data and the predicted values.
Connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi or ensuring that the standard error of the regression equals the standard error of the slope estimator are not the steps involved in deriving the OLS estimator. The OLS method specifically focuses on minimizing the sum of squared residuals.
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at the end of practice, there are 240 ounces of sports drink left in the cooler. every player had some sports drink from the cooler. based on the equation y = 648 - 24x, how many players were at practice?
10
15
17
21
Answer: 17 or C
Step-by-step explanation:
24 times 17 is 408 and 648 - 408 is 240 ounces
Determine an equation for an exponential that model this data set in form p=a(b)^t justify both your values of a and b round b to the nearest hundredth
The equation for an exponential that models this data set is: p = 10(2)^t
To determine an equation for an exponential that models the given data set in the form p = a(b)^t, we first need to identify the values of a and b. To do this, we can use two points from the data set and solve for a and b. Let's choose the points (0, 10) and (2, 40):
When t = 0, p = 10: 10 = a(b)^0 = a
When t = 2, p = 40: 40 = a(b)²
Dividing the second equation by the first, we get:
4 = (b)²
Taking the square root of both sides, we get:
b = 2
Now that we have the value of b, we can use one of the original equations to solve for a:
10 = a(2)^0 = a
So, a = 10.
Therefore, the equation for an exponential that models this data set is:
p = 10(2)^t
We can check this equation by plugging in the other data points and verifying that they satisfy the equation. And rounding b to the nearest hundredth gives us b = 2.00.
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PLEASE HELP WITH 4 AND 5
1. The area of the shaded region is
2. percentage of the shaded part is 89.6%
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The area of the shaded part = area of the rectangle - area of unshaded part
Area of rectangle = 7× 11 = 77 unit²
area of rectangle = 1/2 bh
= 1/2 × 4 × 4
= 1/2 × 8
= 4 unit²
area of second triangle = 4 units²
area of unshaded part = 4+4 = 8 units²
area of shaded part = 77-8 = 69units²
2. percentage of the rectangle shaded = 69/77 × 100
= 6900/77 = 89.6%
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What are the coordinates of the point on the directed line segment from (2, -6) to
(6, 2) that partitions the segment into a ratio of 3 to 5?
Michael and Susan are a combined height of 132 inches. If Michael is 71
inches tall, how tall is Susan?
Answer: 61 in.
Step-by-step explanation:
What you do first is you must find the total number if inches of both humans combined
132 in.
Then, you want to take the 71 in. from Michael's height, and subtract it from the total number.
132
-71
61
----------
61 in. is your answer.
If there are 30 people in a classroom, what is the probability that at least two have the same birthday
The probability that at least two people in a group of 30 have the same birthday is about 0.7063 or 70.63%.
To calculate the probability that at least two people in a group of 30 have the same birthday, we can use the complement rule:
P(at least 2 people have the same birthday) = 1 - P(all people have different birthdays)
The probability that the first person has a unique birthday is 1 (since there are no other people to share with yet).
The probability that the second person also has a unique birthday is 364/365 (since there are now 364 days left out of 365 that they could have a different birthday from the first person).
Similarly, the probability that the third person has a unique birthday is 363/365, and so on. So, we can write:
P(all people have different birthdays) = 1 x 364/365 x 363/365 x ... x 336/365
Using a calculator or computer program, we can evaluate this expression to be approximately 0.2937.
Therefore,
P(at least 2 people have the same birthday) = 1 - 0.2937 = 0.7063
So the probability that at least two people in a group of 30 have the same birthday is about 0.7063 or 70.63%.
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please help i’ll give brainlist :)
1. A forest fire has been burning for several days. The burned area in acres, is given by
the equation y = (4. 800) 2 where d is the number of days since the area of the
fire was first measured
a. Complete the table
b. Look at the value of y = 4,800 2d when d = -1 what does it tell you about the area burned in the fire? what about when d = -3?
c. How much area had the fire burned a week before it measured 4,800 acres, explain your reasoning
The fire had burned half the area (2,400 acres) one week before it measured 4,800 acres.
How to evaluate Days (d) and Burned area (y), the area burned in the fire, and the area the fire has burned a week before it measured 4,800 acres?
a. To complete the table, we substitute the values of d and evaluate the expression for y.
Days (d) Burned area (y)
0 0
1 23,040
2 92,160
3 207,360
4 368,640
b. When d = -1, the value of y = (4,800)^(2*(-1)) = (4,800)^(-2) = 3.255e-8. This value is very small, indicating that the burned area was negligible or not measurable at this point in time.
When d = -3, the value of y = (4,800)^(2*(-3)) = (4,800)^(-6) = 1.130e-34. This value is extremely small, indicating that there was essentially no burned area at this point in time.
c. To determine the number of days before the fire measured 4,800 acres, we need to solve the equation y = (4,800)^2 for d.
4,800^2 = (4,800)^2d
1 = 2dlog(4,800)
d = log(4,800) / (2log(4,800)) = 0.5
Therefore, the fire had burned half the area (2,400 acres) one week before it measured 4,800 acres. This is because the area burned increases quadratically with time, so the area burned one week before is the square root of the area measured at the time.
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What value of k makes the equation true?
k – 3(k + 5) – 0. 5 = 3(0. 25k + 4)
For -10 as the value of k the equation k – 3(k + 5) – 0. 5 = 3(0. 25k + 4) is true.
Given equation is k – 3(k + 5) – 0. 5 = 3(0. 25k + 4)
To solve the equation, firstly we have to solve or open the brackets using the distributive property that is a(x + y) = ax +ay
Thus the equation becomes, k - 3k - 15 - 0.5 = 0.75k + 12
Then we have to take all the terms with k on one side and other on the other or segregate the like terms, the equation now is
k - 3k - 0.75k = 12 + 15 + 0.5
Simplify the equation by adding or subtracting the like terms.
-2.75k = 27.5
Then we divide the coefficient of k by the other side and get our answer
k = 27.5 ÷ (-2.75)
k = -10
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A scale model of a statue has a height of 10 cm. The real statue has a height of 2 m. The model and statue are both made of the same stone which has a density of 2 g/cm(3). The mass of the real statue is 1632 kg. Find the volume of the model in cm(3)
Answer:
102 cm³
Step-by-step explanation:
density = m/v
1 g = 0.001 kg
Volume of real statue = v = m/d = 1632 kg / 0.002 kg/cm³ = 816,000 cm³
scale factor for height: 200 cm : 10 cm = 20 : 1
scale factor for volume: 20³ : 1³ = 8,000 : 1
Volume of model = 816,000 cm³ / 8,000 = 102 cm³
Question 11 (Multiple Choice Worth 5 points)
(Laws of Exponents with Integer Exponents MC)
Choose the expression that is equivalent to
9
92
Therefore, the equivalent expression to [tex]9^2[/tex] is 81.
How to solve equation?To solve an equation, you need to isolate the variable on one side of the equation, typically the left side, and simplify the other side until you are left with an expression that has only the variable you are trying to solve for.
Here are the general steps to solve an equation:
Start by simplifying both sides of the equation as much as possible. This may involve distributing or combining like terms.
Get all terms with the variable you are solving for on one side of the equation. To do this, you can add or subtract terms from both sides of the equation. For example, if you have the equation 2x + 5 = 9, you can subtract 5 from both sides to get 2x = 4.
Isolate the variable by dividing both sides of the equation by its coefficient. In the above example, you can divide both sides by 2 to get x = 2.
Check your solution by plugging it back into the original equation and verifying that both sides of the equation are equal.
[tex]a^m/a^n = a^{(m-n)}[/tex]
to simplify the expression.
The expression [tex]9^2[/tex] means 9 multiplied by itself 2 times:
[tex]9^2 = 9 * 9[/tex]
Using the laws of exponents, we can rewrite this expression as:
[tex]9^2 = 9^{(1+1)} (since 2 = 1 + 1)[/tex]
Then, using the rule that [tex]a^{(m+n)} = a^m * a^n[/tex], we have:
[tex]9^2 = 9^1 *9^1[/tex]
Finally, using the fact that. [tex]a^1 = a[/tex] for any value of a, we get:
We can use the rule of exponents that states:
[tex]9^2 = 9 * 9 = 81[/tex]
Therefore, the equivalent expression to [tex]9^2[/tex] is 81
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The area of a rectangle is represented by the expression x^2-9x+14 units^2. Find the expressions that could represent the length and width of the rectangle
The expressions that could represent the length and width are (x - 2) units and (x - 7) units respectively.
To find the expressions that represent the length and width of the rectangle, we need to factor the given expression.
x² - 9x + 14 = (x - 2)(x - 7)
The length and width of the rectangle are represented by two factors of the expression.
To find the length and width of the rectangle, we need to understand the formula for the area of a rectangle, which is length multiplied by width. The given expression x²-9x+14 represents the area of the rectangle. To find the expressions that represent the length and width, we need to factor the given expression.
We can do this by finding two numbers that multiply to 14 and add up to -9. These numbers are -2 and -7. Therefore, we can factor the given expression as (x - 2)(x - 7). From this, we can see that the length of the rectangle is represented by the factor (x - 2) units and the width is represented by the factor (x - 7) units.
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HELP PLEASE I’m struggling
A) we can forecast that 15,007 will attend this year's county fair.
B) we can expect approximately 1,001 people to receive a prize.
How did we get the above conclusions?Using the attendance data given, we can find the %increase in attendance from year to year as follows
From year 1 to year 2 - (10,365 - 9,278)/9,278
≈ 0.117 or 11.7%
From year 2 to year 3 - (12,128 - 10,365)/10,365
≈ 0.170 or 17.0%
From year 3 to year 4 - (13,304 - 12,128)/12,128
≈ 0.097 or 9.7%
finding the average of the tree percentages, we have
(11.7% + 17.0% + 9.7%)/3 ≈ 12.8 %
So applying this to the last years attenance we have:
1.129 x 13,304 = 15020.216
Or 15,020 since people cannot be in decimal format.
2)
Since the first 20% of people attending the fair will receive a raffle ticket, we can estimate the number of raffle tickets as follows ....
15,007 ×0.20 = 3, 001.4
Now we can estimate the number of people who will receive a prize by taking one-third of the number of raffle tickets...
3,002 ÷ 3 ≈1 ,000.7
which is approximatly 1001 people.
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Gabriella needs 120 meters of fence to surround a rectangular garden.
the length of the garden is three times its width, w.
how wide is the fence?
(please solve how the answer is formatted, i already looked at the other posts people made on this question and they did not help)
Answer is 15 meters
To solve this problem, we can use the formula for the perimeter of a rectangle, which is
P = 2l + 2w,
where P is the perimeter, l is the length, and w is the width.
We are given that Gabriella needs 120 meters of fence, which means that
P = 120.
We are also given that the length of the garden is three times its width, or
l = 3w.
Substituting these values into the formula, we get:
120 = 2(3w) + 2w
Simplifying this equation, we get:
120 = 8w
Dividing both sides by 8, we get:
w = 15
Therefore, the width of the garden is 15 meters.
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Harvey won some money on a
scratch-and-win ticket. Then, he won a
$2 bonus. When he arrived at the counter,
he noticed that he had also won a "triple
your winnings" ticket. As Harvey was
cashing in his prize, the cashier told him
he was the 100th customer, so his total
winnings were automatically doubled. Write two algebraic expressions to
describe Harvey’s winnings
First algebraic expression: x + 2. Second algebraic expression: 6x + 12.
We can represent Harvey's winnings using algebraic expressions.
Let's use the variable 'x' to represent the amount Harvey won on the scratch-and-win ticket. Harvey then won a $2 bonus, so we add 2 to 'x':
1) x + 2
Next, Harvey won a "triple your winnings" ticket, so we need to multiply the current winnings by 3:
2) 3(x + 2)
Finally, as the 100th customer, Harvey's total winnings were doubled:
3) 2 * 3(x + 2)
So, the two algebraic expressions to describe Harvey's winnings are:
1) x + 2 (initial winnings with the $2 bonus)
2) 2 * 3(x + 2) (total winnings after tripling and doubling)
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3 + v = 2 (2v -1) -----------
If the cos= and tan 0 = 1/32,
what is sin 0?
13
The calculated value of sin of the angle is 1/96
Calculating the value of sin of the angleFrom the question, we have the following parameters that can be used in our computation:
cos(θ) = 1/3
tan(θ) = 1/32
The value of sin of the angle is calculated as
sin(θ) = cos(θ) * tan(θ)
substitute the known values in the above equation, so, we have the following representation
sin(θ) = 1/3 * 1/32
Evaluate the products
so, we have the following representation
sin(θ) = 1/96
Hence, the value of sin of the angle is 1/96
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Pairs of twins are numbered 1, 1, 2, 2, and so on seated around a circle so that the least number of gaps between two twins always equals the assigned number. Find two different twin circles with 5 pairs of twins and explain why there is no twin circle with 3 pairs of twins
Therefore , the solution of the given problem of circle comes out to be since the numbers 1, 2, and 3 cannot be dispersed evenly around the circle with the necessary amount of gaps.
What is circle?Each element of the aeroplanes creates a circle when viewed from this new angle and at a distance. (center). Its structure is composed of surfaces and undulating regions that contrast with one another. Additionally, it rotates equally within the centre in all directions. Every ultimate extent of a circular or restricted double sphere is the same as the sphere's "center."
Here,
One potential twin circle that we can create is as follows:
=> 1 2 1 3 2 5 4 5 4 3
Here, the first twin pair 1 is divided into three pairs, with the second twin pair 2 being divided into two pairs, the third twin pair being divided into three pairs, and so on. This satisfies the criteria of the puzzle, and we can verify that every twin pair appears precisely twice.
When the numbers are reversed, a second potential twin circle results:
=> 3 4 5 4 5 2 3 1 2 1
As a result, there is no such twin circle since the numbers 1, 2, and 3 cannot be dispersed evenly around the circle with the necessary amount of gaps.
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pleasee helppp!!!!!!
The volume of the cone with a radius of 8cm and height of 15 cm is V = 1005.3 cm³, so the correct option is C.
How to get the volume of the cone?Remember that for a cone of radius R, and height H, the volume is given by the formula below:
V = (1/3)*pi*R²*H
Where pi = 3.1416
In this case, we know that the radius of the cone is 8cm and the height is 15cm, replacing that in the volume formula we will get:
V = (1/3)*3.1416*(8cm)²*15cm = 1,005.3 cm³
Then the correct option is c.
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30 POINTS!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!
If the measure of arc QR is 40 degrees, what is the measure of angle PQR?
The measure of angle PQR is 20 degrees.
We have,
The measure of angle PQR can be found by using the property that the measure of an inscribed angle is half the measure of its intercepted arc.
Given that the measure of arc QR is 40 degrees, we can conclude that the measure of angle PQR is half of that, which is:
The measure of angle PQR = 1/2 x Measure of arc QR
= 1/2 x 40 degrees
= 20 degrees
Therefore,
The measure of angle PQR is 20 degrees.
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Alan buys a bag of cookies that contains 5 chocolate chip cookies, 5 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies. What is the probability that Alan randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a peanut butter cookie? Express you answer as a reduced fraction
Use the given sample data to find each of the listed values. In your answer, include both numerical answers and an explanation, in complete sentences, for the steps necessary to find the data values. Complete your work in the space provided.
62 52 52 52 64 69 69 76 54 58 61 67 73
Range _____
Q1 _____
Q3 _____
IQR _____
Using the given sample data, the data values are:
Range 24
Q1 52
Q3 69
IQR 17
1. Arrange the data in ascending order:
52, 52, 52, 54, 58, 61, 62, 64, 67, 69, 69, 73, 76
2. Calculate the range (highest value - lowest value):
Range = 76 - 52 = 24
3. Find the first quartile (Q1) - the median of the first half of the data:
Since there are 13 data points, we'll take the median of the first 6 numbers: (52 + 52) / 2 = 52
Q1 = 52
4. Find the third quartile (Q3) - the median of the second half of the data:
We'll take the median of the last 6 numbers: (69 + 69) / 2 = 69
Q3 = 69
5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 69 - 52 = 17
So, the requested values are:
Range = 24
Q1 = 52
Q3 = 69
IQR = 17
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The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
The unique equation of the given parabola in the form of f(x) = (x - a)(x - b) is given by, f(x) = x(x + 6).
The y intercept of the parabola is at (0,0).
Zeros of the parabola are at x = 0, -6.
Given the model equation for the parabola is f(x) = (x - a)(x - b)
It is the standard equation of a parabola with zeros x = a, b.
Here from the graph we can see that at x = -6, 0 the value of y reaches 0 that is the parabola has zeros at x = 0, -6.
So, a = 0 and b = -6
So, f(x) = (x - 0)(x - (-6))
f(x) = x(x + 6)
From the graph we can also see that the parabola is downward negative Y axis.
At y intercepts x = 0
So, the equation becomes in that case,
f(x) = 0.
So (0, 0) is the only y intercept of the parabola.
Hence, the equation of the unique parabola is, f(x) = x(x + 6) and Y intercept is at (0, 0) and zeros are at x = 0, -6.
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The question is incomplete. The complete question will be -
"The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros."
Is the following data an example of a linear function?
Yes, The given table is an example of a linear function.
Since, The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
To check the following data an example of a linear function.
Now, We can check the slope of given tables as;
⇒ Slope = (3 - (- 2)) / (0 - (- 7))
= (5 / 7)
⇒ Slope = (8 - 3) / (7 - 0)
= (5 / 7)
Thus, This table represent the an example of a linear function.
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