The explanation can be given down in details . Using this information
are the key features needed to graph a polynomial function and to find these key features to sketch a rough graph of a polynomial function.
To graph a polynomial function, you need to identify and understand its key features, which include:
Degree: The highest power of the variable in the polynomial determines its degree. For example, a polynomial of degree 3 would have terms like [tex]ax^{3} +bx^{2} +cx+d.[/tex] The degree influences the behavior of the polynomial, such as whether its ends point up or down.
Leading Coefficient: The coefficient of the term with the highest power of the variable. It influences the end behavior of the polynomial, determining whether the graph rises to the left and rises to the right or falls to the left and falls to the right.
Roots (Zeros): These are the values of [tex]x[/tex] for which the polynomial evaluates to zero. They are the points where the graph crosses the [tex]x[/tex]-axis.
Turning Points: Points where the graph changes direction. These occur at local maxima or minima and can be found by setting the derivative of the polynomial equal to zero and solving for [tex]x[/tex].
To sketch a rough graph of a polynomial function, follow these steps:
Determine the Degree and Leading Coefficient: Identify the highest power of the variable and the coefficient of that term.
Find the Roots (Zeros): Set the polynomial equal to zero and solve for
[tex]x[/tex]. These are the points where the graph intersects the x-axis.
Identify Turning Points: Find the critical points by taking the derivative of the polynomial, setting it equal to zero, and solving for
[tex]x[/tex]. Then, use the second derivative test or analyze the behavior of the function around these points to determine whether they are local maxima or minima.
Plot Key Points: Use the roots and turning points to plot key points on the graph.
Consider End Behavior: Determine whether the leading coefficient is positive or negative. If it's positive, the ends of the graph will point upwards; if it's negative, they will point downwards.
Sketch the Curve: Connect the plotted points smoothly, taking into account the behavior of the polynomial between the key points. Make sure to show any symmetry if present and adjust the curvature based on the behavior around turning points.
Optional: Use a Graphing Tool: If available, utilize graphing software or calculators to verify your sketch and refine it if necessary.
By following these steps, you can sketch a rough graph of a polynomial function and visualize its key features effectively.
COMPLETE QUESTION:
What are the key features needed to graph a polynomial function? Explain how to find these key features to sketch a rough graph of a polynomial function.
The Philips family had 3 cats. They needed to split 20 ounces of cat food among the three cats. How much cat food would each cat get? between what two whole numbers does your answer lie?
Each cat would get approximately 6.67 ounces of cat food, which falls between 6 and 7 ounces. The calculation is done by dividing the total amount of food (20 ounces) by the number of cats (3).
Explanation:The Philips family had to split 20 ounces of cat food among their 3 cats. To find out how much food each cat gets, we need to divide the total amount of food by the number of cats. Calculating this, 20 ounces ÷ 3 cats equals approximately 6.67 ounces per cat. Even though this is a decimal, if we consider whole numbers, the amount each cat gets falls between 6 and 7 ounces, since 6.67 is more than 6 and less than 7.
When dealing with fractions and division, it's essential to understand the concept of division and be able to find averages. The task at hand may often find itself related to dividing a quantity evenly among a number of recipients, much like in scenarios where we have to split a pie or determine individual portions.
To divide 20 ounces of cat food equally among three cats, each cat gets approximately 6.67 ounces. The amount of food per cat lies between the whole numbers 6 and 7.
Explanation:The question is asking how to divide 20 ounces of cat food equally among three cats. To find out how much each cat would get, you divide the total amount of cat food by the number of cats:
Determine the total amount of food: 20 ounces.Count the number of cats: 3 cats.Divide the total amount of food by the number of cats: 20 ounces ÷ 3 cats = approximately 6.67 ounces per cat.This calculation shows that each cat would get approximately 6.67 ounces of food. This value lies between the whole numbers 6 and 7. Therefore, when the Philips family divides the cat food, each cat gets a little more than 6 ounces but less than 7 ounces of food.
Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. Use the drop-down menus to identify the steps Lorne used to find the difference. 1. (–3x3 + 5x2 + 4x – 7) + (–6x3 + 2x – 3) 2. (–3x3) + 5x2 + 4x + (–7) + (–6x3) + 2x + (–3) 3. [(–3x3) + (–6x3)] + [4x + 2x] + [(–7) + (–3)] + [5x2] 4. –9x3 + 6x + (–10) + 5x2 5. –9x3 + 5x2 + 6x – 10
To find the polynomial difference, Lorne transformed the subtraction into addition of the opposite, combined like terms, and simplified the expression to get the result of -9x³ + 5x² + 6x - 10.
To find the difference between the two polynomials, Lorne correctly followed the steps of subtraction by changing the subtraction to the addition of the opposite. The process is outlined below:
Add the opposite of the second polynomial to the first polynomial by changing the sign of each term in the second polynomial.
Combine like terms by adding the coefficients of terms with the same degree of x.
Rearrange the terms in descending order of their degrees.
Write down the final simplified form of the polynomial.
By following these steps, the result would be:
Step 1:
(-3x³ + 5x² + 4x - 7) + (-6x³ + 2x - 3)
Step 2:
(-3x³ + 5x² + 4x - 7) + (-6x³) + 2x + (-3)
Step 3:
[(-3x³) + (-6x³)] + [4x + 2x] + [(-7) + (-3)] + [5x²]
Step 4:
-9x³ + 6x + (-10) + 5x2
Step 5:
-9x³ + 5x² + 6x - 10
Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]
The steps Lorne used to find the difference between [tex]-3x^{3} +5x^{2} +4x-7[/tex] and [tex]6x^{3} -2x+3[/tex] are:
[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]
So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]
Lorne first added the two polynomials by combining like terms, then simplified the result by collecting like terms. The final expression represents the difference between the two polynomials after combining and simplifying.
COMPLETE QUESTION:
Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. Use the drop-down menus to identify the steps Lorne used to find the difference.
[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]
The system of equations 4x-y=4(x+1) , y = 6 has:
A. one solution
B. infinitely many solutions
C. no solution
The system of equations 4x-y=4(x+1) and y=6 has no solution.
To determine the solution(s) of the system of equations, let's analyze each equation:
Equation 1: 4x - y = 4(x + 1)
Equation 2: y = 6
To simplify Equation 1, we can distribute 4 on the right side:
4x - y = 4x + 4
By rearranging terms, we have:
- y = 4
Comparing Equation 2 with this result, we see that the two equations are contradictory. Equation 2 states that y = 6, while the modified Equation 1 states that y = -4. This means there is no value of y that can simultaneously satisfy both equations.
Thus, the system of equations has no solution.
Therefore, the correct answer is C. no solution.
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You have a $50 gift card to the same site. You want to buy an album with 16 tracks for $12.99 and then use the rest of the gift card for single tracks. How many songs can you buy with the gift card?
Final answer:
After purchasing an album for $12.99 from the $50 gift card, the remaining balance is $37.01, which allows the purchase of 37 more single tracks, assuming each track costs $1.
Explanation:
To determine how many songs can be bought with a $50 gift card after purchasing an album for $12.99, we need to subtract the cost of the album from the total amount on the gift card. So, we have:
Total amount on gift card: $50Cost of album: $12.99Subtracting the cost of the album from the gift card amount gives us:
$50 - $12.99 = $37.01
Assuming that each single track costs $1 as per the scenario provided, we can divide the remaining balance by the cost per single track:
$37.01 ÷ $1 per track = 37 tracks
This means that you can purchase 37 more single tracks with the remaining balance on the gift card.
the area of this circle is 72π m^2 what is the area of a 45° sector of this circle
need help solving this
what is 3 fifths times one and 1third
Mel Sturbridge needs $24,700 to remodel his home.
Find the face value of a simple discount note that will provide the $24,700 in proceeds if he plans to repay the note in 180 days and the bank charges an 8% discount rate.
Round to the nearest cent.
To find out the face value of a simple discount note that will provide a proceed of $24,700 with an 8% discount rate for 180 days, use the formula FV = P / (1 - (r * t)). Plug in the given values and compute the answer. The result is the required face value and should be rounded to the nearest cent.
Explanation:To find out the face value of a simple discount note, we can use the formula FV = P / (1 - (r * t)) where FV represents the face value, P is the proceeds, r is the discount rate, and t is the time in years.
In the problem, P = $24,700, r = 8% or 0.08 (expressed as a decimal), and t = 180/365 because there are 365 days in a year and the note is for 180 days. Let's substitute these values into the formula:
FV = 24700 / (1 - (0.08 * (180/365))
When you calculate the expression on the right, the answer will be the face value required to get a proceed of $24,700 with an 8% discount rate for 180 days. Round to the nearest cent for your final answer.
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A bakery makes 640 muffins everyday. which equation shows how to find the number of muffins the bakery makes in a week?
Last summer we took an auto trip of 3427 miles . After we had driven 1578 miles , how many are left ?
max has 2/3 lb. of chocolate. He wants to hand out the chocolate in packages to give to his friends he would like to put 1/6 lb. of chocolate. How many packages can Max make? solve with a visual model
What is the completely factored form of x2y – 2xy – 24y?
Answer:
C: y(x + 4)(x – 6)
Step-by-step explanation:
I took the test on Edge -2022
Sam is training for an upcoming wrestling match. He trains for 3.5 hours each day Monday through Wednesday. He trains 2.5 hours on Thursday and Friday. How many hours will he train if he trains for six weeks
Make a line graph of the data in the table and conjecture on the minimum degree of a polynomial model...
The quadratic equation y = 2(x – 2)2 + 2 with no real solution is graphed. Which value of k will change the function to one with exactly one solution?
On the attached diagram red curve is the graph of the quadratic function [tex]y = 2(x - 2)^2 + 2.[/tex] As you can see this graph has no intersections with x-axis, this means that there are no solutions.
If you translate red curve 2 units down, you obtaine the graph (blue curve) of the function [tex]y = 2(x - 2)^2[/tex] and this graph has one common point with x-axis. This means that there will be exactly one solution.
Answer: k=-2 (you add -2 to the function [tex]y = 2(x - 2)^2 + 2[/tex] to obtain the function [tex]y = 2(x - 2)^2[/tex]).
Answer: 0 ZERO
Step-by-step explanation:
Use Cavalieri’s Principle to calculate the exact volume of an oblique cylinder with a height of 10 meters and a circular base with a radius of 8 meters
Answer: Volume of an oblique cylinder is 2011.43 sq.m.
Step-by-step explanation:
Since we have given that
Radius of a cylinder = 8 meters
Height of a cylinder = 10 meters
Cavelieri's Principle states that volume of an oblique cylinder is same as the volume of right circular cylinder with equal radius and height.
As we know the formula for "Volume of cylinder":
[tex]Volume=\pi r^2h\\\\V=\frac{22}{7}\times 8\times 8\times10\\\\V=\frac{14080}{7}\\\\V=2011.43[/tex]
Hence, Volume of an oblique cylinder is 2011.43 sq.m.
three friends are in the same algebra class. Their scores on a recent test are three consecutive odd intergers whose sum is 279. find each score
If x = 30, what does 55 + x - 27 equal?
Answer:
58
Step-by-step explanation:
Put 30 where x is in the expression and do the arithmetic.
55 + 30 - 27 = 85 - 27 = 58
__
It can be advantageous to use the associative property of addition to evaluate the expression as ...
55 + (30 -27) = 55 +3 = 58
You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent. If necessary round your answer to the nearest hundredth.
The probability of spinning an odd number, flipping heads, then spinning a yellow is ????
probability = number of favourable outcomes / total number of outcomes
probability of spinning any number = 1/3
probability of tossing a coin = 1/2
probability of compound event = 1/3 * 1/2 * 1/3 = 1/18
probability of spinning an odd number, flipping heads, then spinning a yellow is = 2/3*1/2*1/3 = 1/9
25 less than 6 time a number is 107. What is the number? How do you do that?
25 less than 6 times a number is 107 then that number will be 22 it can be determined by the formation of the equation.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say that number is x
6 times x number
⇒ 6x
25 less than 6x
⇒ 6x - 25
It is equal to 107
So,
6x - 25 = 107
6x = 132
x = 132/6
x = 22
Hence "25 less than 6 times a number is 107 then that number will be 22".
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Find |p|.....................
7b divided by 12=4.2 what is b
To solve for b in the equation 7b divided by 12 equals 4.2, multiply both sides by 12 and then divide by 7, resulting in b being equal to 7.2.
Explanation:To solve the equation 7b ÷ 12 = 4.2 for b, we must isolate b on one side of the equation. We can begin by multiplying both sides of the equation by 12 to cancel out the division by 12 on the left side. This results in the equation 7b = 4.2 × 12. To find the value of b, we then divide both sides of the equation by 7:
Multiply both sides by 12: 7b ÷ 12 × 12 = 4.2 × 12Simplify: 7b = 50.4Divide both sides by 7: 7b ÷ 7 = 50.4 ÷ 7b = 7.2Therefore, the value of b is 7.2.
To find the value of b in the equation 7b/12 = 4.2, multiply both sides by 12 and then divide by 7 to get b = 7.2. The value of b is 7.2.
Explanation:The student is asking how to find the value of b in the equation 7b divided by 12 equals 4.2. To solve for b, you can follow these steps:
Write down the original equation: 7b / 12 = 4.2.Multiply both sides of the equation by 12 to eliminate the denominator: 12 * (7b / 12) = 12 * 4.2, which simplifies to 7b = 50.4.Divide both sides by 7 to solve for b: 7b / 7 = 50.4 / 7, which gives b = 7.2.Therefore, the value of b is 7.2.
Mr. Harrow has eight boys and six girls in his Honors Precalculus class. If he randomly chooses two students, one at a time, what is the probability that they are both girls
What is the area of the figure?
Express your answer as a mixed number in simplest form.
? m2
Find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywehere to the right of a 2
To find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywhere to the right of a 2, we can consider two cases depending on the last digit being 0 or 2.
Explanation:To find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywhere to the right of a 2, we can break the problem down into two cases: when the last digit is 0 or when the last digit is 2. If the last digit is 0, then the number of n-digit ternary sequences is equal to the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2. If the last digit is 2, then the number of n-digit ternary sequences is equal to the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2, plus the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2.
A Bird Is flying 5 m/s. How far will it travel if it flies for 3minutes
A. 15m
B. 5m
C. 900m
D. 36m
Write 4/10 as a fraction with a denominator of 100. Then write 4/10 as a decimal.
Would it be 4/100 or 40/100? The decimal would be 0.4 ?
Philip is going on a 400040004000-kilometer road trip with three friends. The car consumes 666 liters of gas per 100100100 kilometers, and gas costs \$1.50$1.50dollar sign, 1, point, 50 per liter.
Help with this question
complete the ordered pair for the given equation. (_,-1);y=-3/5x-7