This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (2, minus 8) with the left slope at (0, 0) and the right slope at (4, 0).
f(x) = x
(x −
)
f(x) =
(x −
)2 +
Answers
Answer:
\(\textsf{Factored form}: \quad f(x)=2x(x-4)\)
\(\textsf{Vertex form}: \quad f(x)=2(x-2)^2-8\)
Step-by-step explanation:
Factored form of a quadratic function
\(f(x)=a(x-p)(x-q)\)
where:
p and q are the x-interceptsa is some constantGiven x-intercepts:
(0, 0)(4, 0)Therefore:
\(\implies f(x)=a(x-0)(x-4)\)
\(\implies f(x)=ax(x-4)\)
To find a, substitute the given vertex (2, -8) into the equation and solve for a:
\(\implies 2a(2-4)=-8\)
\(\implies -4a=-8\)
\(\implies a=2\)
Therefore, the function's equation in factored form is:
\(f(x)=2x(x-4)\)
Vertex form of a quadratic equation
\(f(x)=a(x-h)^2+k\)
where:
(h, k) is the vertexa is some constantGiven:
vertex = (2, -8)Therefore:
\(\implies f(x)=a(x-2)^2-8\)
To find the constant a, substitute one of the x-intercepts into the equation and solve for a:
\(\implies a(0-2)^2-8=0\)
\(\implies 4a-8=0\)
\(\implies a=2\)
Therefore, the function's equation in vertex form is:
\(f(x)=2(x-2)^2-8\)
x intercepts=0,4
So the equation
y=a(x-b)(x-c)y=ax(x-4)Now put vertex and find a
-8=a(2)(2-4)-8=2a(-2)a=-8/-4a=2So equation
y=2x(x-4)Related Questions
Find the value when x= 2 and y =3.
2x⁰ y-²
1/9
2/9
-18
Answers
Answer:
36
Step-by-step explanation:
Answer:
The answer is 2/9
Step-by-step explanation:
2(2)^0 (3)^-2 = 2(1)/(3)^2 = 2/9
please i will give you brainly -1,8÷9 I need step by step
Answers
Answer:
-0.2
I couldn't get step by step but hope this answer helps out a little...
(Do you need it for ur assignment?)
Step-by-step explanation:
-18/9 = 2, 9 goes into 18, 2 times, but a negative divided by a positive always = a negative number so the answer would come out to be -2.
-18/9 = 2, 9 goes into 18, 2 times, but a negative divided by a positive always = a negative number so the answer would come out to be -2.
however is you were typing -1.8 / 9 then it would be -0.2. Multiplying -0.2 * 9 would give you -1.8. Same rule applies as to why it's negative
I wasn't sure if the comma was a typo in your question but I Hope this helps :)
fine the nth term of 11,13,15,17
Answers
The nth term of 11,13,15,17 is,
⇒ T (n) = 9 + 2n
Given that;
The sequence is,
11, 13, 15, 17, ....
Here, Common difference is,
13 - 11 = 2
15 - 13 = 2
Hence, Sequence is in Arithmetic sequence.
So, the nth term of 11,13,15,17 is,
⇒ T (n) = a + (n - 1)d
⇒ T (n) = 11 + (n - 1) 2
⇒ T (n) = 11 + 2n - 2
⇒ T (n) = 9 + 2n
Thus, The nth term of 11,13,15,17 is,
⇒ T (n) = 9 + 2n
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What is the domain of the equation?
Answers
The domain of the equation include the following: D. all real numbers.
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-∞, ∞] or all real numbers.
Range = [-4, ∞}
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2. The mean temperature in an area is 74 degrees Fahrenheit. The sum of the temperatures is
2,516. How many temperatures are in the set?
Answers
To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.
Number of temperatures = Sum of temperatures / Mean temperature
In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.
Number of temperatures = 2,516 / 74
Calculating the division:
Number of temperatures ≈ 34.05
Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.
in the classic arcade game donkey kong, the code calculates the time allowed per level by multiplying the current level by 10 and adding 40. on level 22, that calculated time is 260. however, the game displays a time of 4 instead of 260. it is impossible for anyone to complete the level in just 4 seconds, so no player ever makes it past level 22.
Answers
As per the unitary method, the most likely cause of the level 22 bug is internal error overflow.
Unitary method is a mathematical technique used to convert a given number into its smallest unit form.
Donkey Kong's Level 22 bug is a confusing one since the code calculates the time allowed per level correctly with the unitary method.
The most likely cause of this bug is the unitary method.
The unitary method multiplies the given number by 10 and adds 40, then divides the result by ten to get the time expressed in seconds.
However, the game was likely written in a language that does not recognize the unitary method, leading to the result being expressed in minutes instead of seconds.
As a result, when level 22 is loaded, the game calculates the time correctly (260 seconds) but displays the answer in minutes (4 minutes) instead.
This makes it impossible for anyone to complete the level in just 4 seconds, explaining why no player ever makes it past level 22.
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Which function has a greater maximum?
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=
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f(x)=−2(x+4)
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A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens down. The function increases through negative four, negative five and negative three, negative two. It has a maximum at negative two, one, then the function decreases through negative one, negative two and zero, negative five.
Answers
The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.
1. The given function is f(x) = \(-2(x+4)^2\) + 1.
2. To find the maximum of the function, we need to determine the vertex of the parabola.
3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.
4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.
5. The x-coordinate of the vertex is given by h = -4.
6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.
7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.
8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).
9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.
10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.
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Find all the zeros of f(x) help please
Answers
Since \(f(6)=0\), by the remainder theorem this means that x - 6 divides f(x) exactly. This means there are constants a, b, and c such that
\(\dfrac{f(x)}{x-6} = ax^2 + bx + c\)
Multiplying both sides by x - 6 gives
\(f(x) = (x-6)(ax^2+bx+c) \\\\ 2x^3-19x^2+45x-18 = ax^3 + (b-6a)x^2 + (c-6b)x - 6c\)
Then a, b, c satisfy
\(\begin{cases}a=2 \\ b-6a=-19 \\ c-6b=45 \\ -6c=-18\end{cases}\)
and solving this system gives a = 2, b = -7, and c = 3.
So, we have
\(2x^3-19x^2+45x-18 = (x - 6) (2x^2 - 7x + 3)\)
The quadratic term can be factored as
\(2x^2 - 7x + 3 = (2x - 1)(x - 3)\)
which leaves us with
\(f(x) = (x-6)(2x-1)(x-3)\)
so that the zeros of f(x) are 6, 1/2, and 3.
Solve for x 9x=-81
X=-90
X=-72
X=-9
X=-8
Answers
Answer:
x = -9
Step-by-step explanation:
hope this was helpful!! c:
Answer:
x= -9
Step-by-step explanation:
9x/9= -81/9
x= -9
I Need Help Fast??
25=
Answers
This is because 5x5=25
Round to the nearest given place.
1.15294 thousandths
Answers
1.15294
2 is thousandths place, so
1.153
Answer: 1.153
Answer:
1.15294
I hope this answers your question please consider giving me brainliest :)
Please answer immediately I beg.
A pyramid and a cone have the same base area and height. The volume
of the pyramid is 175m³. What is the volume of the one? Explain your answer.
Answers
The volume of cone is 175 m³
Firstly,
Volume of Pyramid.
The volume (V) of a pyramid is
V = ⅓Ah
Data:
V = 175m³
Calculation:
175 = ⅓× A× h
Ah = 175*3
Ah = 525m³
Secondly,
The volume (V) of a cone is
V = ⅓Ah
Data:
Ah = 525 m³
Calculation:
V = ⅓ A× h
V = 175 m³
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Solve the system of equation using elimination
Answers
Answer:
To Solve a System of Equations by Elimination
Write both equations in standard form. ...
Make the coefficients of one variable opposites. ...
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
here! ( happy hoildays!)
Which graph represents the solution set of the compound inequality below?
x+3<= (4x-12) < 20
OH
4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12
6 7 8 9 10 11 12 13 14
6 7 8 9 10 11 12 13 14
Answers
A graph that represents the solution set of the compound inequality is: graph D.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Next, we would solve the given compound inequality by making x the subject of formula as follows;
x + 3 < 1/2(4x - 12) < 20
Multiplying all through by 2, we have the following:
2x + 6 < 4x - 12 < 40
Next, we would solve the compound inequality in parts:
2x + 6 < 4x - 12
4x - 2x < 12 + 6
2x < 18
x < 18/2
x < 9.
4x - 12 < 40
4x < 40 + 12
4x < 52
x < 52/4
x < 13.
In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).
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53/6 + something = 8
Answers
Answer: -5/6
Step-by-step explanation: 53/6= 8 5/6 -5/6=8
Stephanie has a spinner with sections labelled 1, 2 and 3.
She spun it 100 times and recorded how many times it landed on each section in
the table below.
Work out the relative frequency of landing on an odd number, giving your answer
as
a) a fraction in its simplest form.
b) a decimal.
Section
1
Frequency 17
2
20
3
63
Answers
Answer:
\(\frac{4}{5}\)
0.8
Step-by-step explanation:
Happy to help:)
how do i find the measure of these? i’m lost in math
Answers
Answer: Answers and work are all in the picture that I attached. Hope this helps
state where the function is continuous, discontuous and the type of discontinuity for each
Answers
For x = 2
\(\lim _{x->2^-}(\frac{x}{x-2})=-\infty\)\(\begin{gathered} \lim _{x->2^+}(6)=6 \\ \end{gathered}\)Since:
\(\lim _{x->2^+}f(x)\ne\lim _{x->2^-}f(x)\)The function is discontinuous at x = 2. Besides since the function has a vertical asymptote on one of the sides, we can conclude it is a infinite discontinuity.
For x = 6:
\(\lim _{x->6^-}6=6\)\(\lim _{x->6^+}\frac{x-2}{x^2-6x+8}=\lim _{x->6^+}\frac{x-2}{(x-2)(x-4)}=\lim _{x->6^+}\frac{1}{x-4}=\frac{1}{2}\)Since:
\(\lim _{x->6^+}f(x)\ne\lim _{x->6^-}f(x)\)The function is discontinuous at x = 6, at this point the function has a jump discontinuity
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
Answers
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
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N
m
4
5
4
U
-
3-
Cu v
-5-4-3-2-1
2
-2
1 w
60
r
2345x
What is the domain of the function on the graph?
O all real numbers
O all real numbers greater than or equal to-2
O all real numbers greater than or equal to-5
O all real numbers greater than or equal to 0
Help please
Answers
Answer:
Step-by-step explanation:
Question
N
m
4
5
4
U
-
3-
Cu v
-5-4-3-2-1
2
-2
1 w
60
r
2345x
What is the domain of the function on the graph?
O all real numbers
O all real numbers greater than or equal to-2
O all real numbers greater than or equal to-5
O all real numbers greater than or equal to 0
Help please
Subtract. Write the difference in simplest form.
(5n - 3) - (-2n + 7)
Answers
Answer:
Simplifying
(5n + -3) + -1(-2n + 7) = 0
Reorder the terms:
(-3 + 5n) + -1(-2n + 7) = 0
Remove parenthesis around (-3 + 5n)
-3 + 5n + -1(-2n + 7) = 0
Reorder the terms:
-3 + 5n + -1(7 + -2n) = 0
-3 + 5n + (7 * -1 + -2n * -1) = 0
-3 + 5n + (-7 + 2n) = 0
Reorder the terms:
-3 + -7 + 5n + 2n = 0
Combine like terms: -3 + -7 = -10
-10 + 5n + 2n = 0
Combine like terms: 5n + 2n = 7n
-10 + 7n = 0
Solving
-10 + 7n = 0
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Add '10' to each side of the equation.
-10 + 10 + 7n = 0 + 10
Combine like terms: -10 + 10 = 0
0 + 7n = 0 + 10
7n = 0 + 10
Combine like terms: 0 + 10 = 10
7n = 10
Divide each side by '7'.
n = 1.428571429
Simplifying
n = 1.428571429
Answer:
79-10
Step-by-step explanation:
Brainliest please.
If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values Σx = 2769 and Σx2 = 132,179 to compute the sample mean and sample standard deviation. (Round s to four decimal places.)
Answers
By using a statistical calculator, the actual sample mean and sample standard deviation are:
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
How to calculate the sample mean for the set of data?In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:
Mean = ∑x/(n - 1)
∑x represents the sum of all data values.(n - 1) represents the number of data contained in a sample.In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:
Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)
x represents the observed values of a sample.\(\bar{x}\) is the mean value of the observations.N represents the total number of of observations.By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
I need it done very quick pls help
Answers
Which expression is equivalent to cos(40°)cos(10") + sin(40°)sin(10º)?
O sin(40° – 10°)
O cos(40° + 10º)
O sin(40° + 10º)
O cos(40° – 10º)
Answers
Answer:
The equivalent expression is cos(40° – 10º) ⇒ D
Step-by-step explanation:
The rule of cosine the compound angles is
cos (A + B) = cos A cos B - sin A sin B
cos (A - B) = cos A cos B + sin A sin B
Let us use these rules to solve the question
∵ cos(40°)cos(10°) + sin(40°)sin(10º)
∵ The middle sign is plus
∴ We will use the 2nd rule above
→ Compare the rule by the given expression to find the value of A and B
∵ A = 40° and B = 10°
∴ cos (A - B) = cos (40° - 10°)
∴ cos (40° - 10°) = cos(40°)cos(10°) + sin(40°)sin(10º)
∴ The equivalent expression is cos(40° – 10º)
What is the slope of a line perpendicular to the line whose equation is x-4y=-12. Fully reduce your answer. no varibles are allowed in the answer. first to answer correctly gets brainliest.
Answers
We have x - 4y = -12, let’s make it in the form y = mx + c
4y = x+12
y = (1/4)x + 3
The slope of this line is (1/4)
Slope of perpendicular line will be -4
Choose the greatest fraction.
A) 1/2
B) 1/3
C) 1/4
D) 1/5
Answers
Answer:
1/5 is the answer
Step-by-step explanation:
its the greatest fractions, out of the options you picked
that would be b
Step-by-step explanation:
I hope this helps you and have a nice day
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
9,16,23,...
Find the 46th term.
Answers
The 46th term of the sequence is 324.
We have,
To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.
Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference
of 7.
To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:
a(n) = a(1) + (n - 1) d
where a(1) is the first term, d is the common difference, and n is the term number we want to find.
Using the given information, we have:
a(1) = 9
d = 7
n = 46
Plugging these values into the formula, we get:
a (46) = 9 + (46 - 1)7
a (46) = 9 + 45 (7)
a(46) = 9 + 315
a(46) = 324
Therefore,
The 46th term of the sequence is 324.
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Question 2 A man ran 20 miles in 2 hours. Calculate the average time that it took the man to run each mile in minutes.
Answers
Answer:
6 mintutes per mile
Step-by-step explanation:
find how many minutes are in 2 hours which is 120 then divide that by 20 to get a total of 6
Name the property of multiplication that is shown by the equation 4x· 1 = 4x
Answers
What is the circumference of this circle, in centimeters?
Answers
Answer:
65.9 so it rounds to 66cm