Parabola in the form x^2=4pyIdentify Vertex, value of P, focus, and focal diameter.Identify endpoints of latus rectumWrite equations for the directrix and axis of symmetry X^2= -12y
Answers
Answer:
(a)
• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
• The focus is at (0,-3).
,• The focal diameter is 12
(b)The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
(c)See Graph below
(d)
• I. The equation for the directrix is y=3.
,• II. The axis of symmetry is at x=0.
Explanation:
Given the equation of the parabola:
[tex]x^2=-12y[/tex]For an up-facing parabola with vertex at (h, k) and a focal length Ipl, the standard equation is:
[tex](x-h)^2=4p(y-k)[/tex]Rewrite the equation in the given format:
[tex]\begin{gathered} (x-0)^2=4(-3)(y-0) \\ \implies(h,k)=(0,0) \\ \implies p=-3 \end{gathered}[/tex]• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
The focus is calculated using the formula:
[tex]\begin{gathered} (h,k+p) \\ \implies Focus=(0,0-3)=(0-3) \end{gathered}[/tex]• The focus is at (0,-3).
Focal Diameter
Comparing the given equation with x²=4py, we have:
[tex]\begin{gathered} x^2=4ay \\ x^2=-12y \\ 4a=-12 \\ \implies a=-3 \\ \text{ Focal Diameter =4\mid a\mid=4\mid3\mid=12} \end{gathered}[/tex]The focal diameter is 12
Part B (The endpoints of the latus rectum).
First, rewrite the equation in the standard form:
[tex]\begin{gathered} y=-\frac{1}{12}x^2 \\ \implies a=-\frac{1}{12} \end{gathered}[/tex]The endpoints are:
[tex]\begin{gathered} (a,2a)=(-\frac{1}{12},-\frac{1}{6}) \\ (a,-2a)=(-\frac{1}{12},\frac{1}{6}) \end{gathered}[/tex]The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
Part C
The graph of the parabola is given below:
Part D
I. The equation for the directrix is of the form y=k-p.
[tex]\begin{gathered} y=0-(-3) \\ y=3 \end{gathered}[/tex]The equation for the directrix is y=3.
II. The axis of symmetry is the x-value at the vertex.
The axis of symmetry is at x=0.
Related Questions
Label each point on the number line with the correct value
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By converting fraction to decimal, it is obtained that
a = [tex]-\frac{7}{3}[/tex]
b = [tex]-2\frac{5}{8}[/tex]
c = -2.9
What is decimal and fraction?
Suppose there is a collection and a part of collection has to be taken. The part which is taken is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
Decimal numbers are those numbers which consist of an integer part and a fractional part.
Decimal are of two types-
Terminating decimals are those decimals which has finite number of figures after decimal point
Non terminating decimals are those decimals which has infinite number of figures after decimal point.
Here, the fraction needs to be converted to decimal
[tex]-\frac{7}{3} =[/tex] -2.33 which lies between -2 and -2.5. So Point c is [tex]-\frac{7}{3}[/tex]
[tex]-2\frac{5}{8} =[/tex] -2.625 which lies between -2.5 and -2.9. So point b is [tex]-2\frac{5}{8}[/tex]
Point a is -2.9
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Find the number of distinct arrangements of 12 letters in REENGINEERED. Two of the same letter are considered identical
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We have to find the number of distinct arrangements of 12 letters in REENGINEERED.
First, we list the number of unique letters we have and its frequency. We have:
• R: 2
,• E: 5
,• N: 2
,• G: 1
,• I: 1
,• D: 1
for a total of 12 letters.
We can then calculate the number of distinct arrangements as the the total number of arrangements divided by the permutations that are repeated.
This can be expressed as the factorial of 12 divided by the product of the factorial of the frequencies of each letter (the letters that have a frequency of 1 will not affect the result so they are ignored for the denominator):
[tex]n=\frac{12!}{2!5!2!}=\frac{479001600}{2*120*2}=\frac{479001600}{480}=997920[/tex]Answer: there are 997,920 distinct arrangements.
Answer below due to inability to type out the following question.
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ANSWER
[tex]11.04\text{ or }\frac{-2+\sqrt{580}}{2}[/tex]EXPLANATION
Given that:
In the figure provided, the triangle EFG is similar to the triangle is ECD
FE = 12
CD = 12
FG = CF + 2
To find the length CF, apply the similarity triangle theorem
[tex]\frac{\text{ FE}}{\text{ CF}}\text{ }=\frac{\text{ FG}}{CD}[/tex]Substitute the given data into the above equation
[tex]\begin{gathered} \text{ }\frac{12}{CF}=\frac{CF+2}{12} \\ \text{ cross multiply} \\ \text{ 12}\times12\text{ }=\text{ CF\lparen CF + 2\rparen} \\ \text{ 144 }=\text{ CF}^2\text{ }+\text{ 2CF} \\ CF^2\text{ }+\text{ 2CF -144 =0} \\ \text{ Find CF using the general formula} \\ x\text{ }=\text{ }\frac{-b\pm\sqrt{b^2-\text{ 4ac}}}{\placeholder{⬚}} \\ \text{ a }=1,\text{ b}=2,\text{ c}=-144 \\ \text{ x }=\frac{-2\text{ }\pm\sqrt{2^2-4\times1\times(-144)}}{2} \\ \text{ x}=\text{ }\frac{-2\pm\sqrt{4+576}}{2} \\ \text{ x }=\text{ }\frac{-2\pm\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+24.083}{2} \\ \text{ x }=\frac{22.083}{2} \\ \text{ x }=11.04 \\ \text{ Therefore, CF is 11.04 or }\frac{-2+\sqrt{580}}{2} \end{gathered}[/tex]I need help solving this problem. My answer isn’t coming out right. I have to find the missing length.
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From the given diagram we get that the lines marked with the arrow are parallel, then the two triangles are similar.
To answer this question we will use the following diagram as a reference:
Therefore:
[tex]\frac{?}{18}=\frac{9-4}{9}.[/tex]Simplifying the above result we get:
[tex]\frac{?}{18}=\frac{5}{9}.[/tex]Multiplying the above result by 18 we get:
[tex]\frac{?}{18}\times18=\frac{5}{9}\times18.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} ?=\frac{90}{9}, \\ ?=10. \end{gathered}[/tex]Answer:
[tex]?=10.[/tex]resultado de w+2 1/2=3 1/2
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We need to solve the following expression:
[tex]w+2\frac{1}{2}=3\frac{1}{2}[/tex]To do that we have to isolate the w variable on the left side of the equal sign, this is done by changing the signal of the constant number as shown below:
[tex]w=3\frac{1}{2}-2\frac{1}{2}[/tex]We can now subtract the two mixed fractions to determine the value of w.
[tex]\begin{gathered} w=3\text{ + }\frac{1}{2}-(2+\frac{1}{2}) \\ w=3-2+\frac{1}{2}-\frac{1}{2}=1 \end{gathered}[/tex]The value of w is 1.
A box of pencils weighed 2.81 grams. If a principal ordered 38 boxes, how much would they weigh?
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Answer:106.78
(If this answer is wrong, please message me and I will try to fix it)
Step-by-step explanation: let's take 2.81 grams, if you times that by 38 boxes, you will get 106.78 grams.
Could you explain the following:Use s=rwt to find the value of the missing variable.S=pi/5m, r=7m, t=2sec
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Answer:
[tex]0.0449[/tex]Explanation:
Here, we want to find the value of the missing variable w
We start by substituting the individually given values as follows:
[tex]\begin{gathered} \frac{\pi}{5}\text{ = 7}\times w\times2 \\ \\ w\text{ = }\frac{\pi}{5\times7\times2}\text{ = 0.0449} \end{gathered}[/tex]
Clara likes the buffet option of chicken, swordfish, roasted potatoes, and brussels sprouts
for $23 per person. She does not think everyone will eat the swordfish, so she decides to
only do a half portion of swordfish per guest, which means half the price. If the original
price of the swordfish was $7 per guest, what will the new overall price of the buffet be
per person?
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The unitary method is used to find the unit value of the quantity. The price for the buffet after taking half portion of swordfish will be $19.5.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The price for complete buffet is $23 per person.
The price for swordfish per guest is $7.
Then, the price for half portion swordfish is $7 / 2 = $3.5.
Now, the price of buffet without swordfish is $23 - $7 = $16.
Thus, after taking only half portion of swordfish the new price becomes,
$16 + $3.5 = $19.5
Hence, the new price of the buffet for each person will be $19.5.
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3 parts!!! Suppose that on January 1 you have a balance of $4500 on a credit card whose APR is 12%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1.a. Calculate your monthly payments.b. When the card is paid off, how much will you have paid since January 1?c. What percentage of your total payment from part(b) is interest?Part A: The monthly payment is ?(Do not round until the final answer. Then round to the nearest cont as needed.)
Answers
Given,
P=$4500
r=12%
For 1 month the rate is 12/12%=1%
So interest for one month is
[tex]I=\frac{4500\times1\times1}{100}=45[/tex]a. The monthly payment is:
[tex]\begin{gathered} A=\frac{4500\times0.01\times(1+0.01)^{12}}{(1+0.01)^{12}-1} \\ \Rightarrow A=\frac{50.70}{0.12} \\ \Rightarrow A=422.5 \end{gathered}[/tex]The monthly payment is $422.5
b. Total payment for a year is:
A=4500+(12x45)=$5040
Total amount paid since January is $5040
c. The percentage of interest is:
[tex]\frac{45\times12}{5040}\times100\%=10.71[/tex]The percentage interest is 10.71%
Based on the density graph below, what is the probability of a valuein the sample space being anywhere from 0 to 20?
Answers
Answer
Option A is correct.
Probability of a value in the sample space being anywhere from 0 to 20 = 80%
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
For this question,
Number of boxes from 0 to 20 = 20
Total number of boxes in the density graph = 25
Probability of a value in the sample space being anywhere from 0 to 20 = (20/25) = 0.8 = 80%
Hope this Helps!!!
The point (7,-2) is a point on the graph of y=f(x)B) write the function that would shift (7,-2) right 3 then up 4
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B) We have to find a function that would shift (7,-2) 3 units to the right and 4 units up.
To move a function in the horizontal axis, we have to add or substract the numbers of units in the argument:
f(x-k) will translate f(x) "k" units to the right. If "k" is negative, the function will be translated "k" units to the left.
Then, if we need to translate the point 3 units to the right, f(x) should have an argument of (x-3).
If we have to translate it in the vertical axis, we just add or substract outside f(x).
For example, f(x)+h will translate f(x) "h" units up. If "h" is negative, it will be translated down.
In this case, as we have to translate the function 4 units up, we add 4 outside of f(x).
Combining the two translations, we get:
[tex]y=f(x-3)+4[/tex]Answer:
B) The function that translates the function 3 units right and 4 units up is y = f(x-3)+4.
The number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs0123stP(x)0.620.240.070.05.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?
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a sphere has radius 3xcm. write down an expression for the surface area of the sphere in terms of x.give your answer in the simplest form
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The expression to obtain the surface area of a sphere is
[tex]A=4\cdot\pi\cdot r^2[/tex]If the radius is equal to 3x cm then the expression is
[tex]A=4\cdot\pi\cdot(3x)^2[/tex]square the 3x
[tex]\begin{gathered} A=4\cdot\pi\cdot(3^2)\cdot x^2 \\ A=4\cdot\pi\cdot9\cdot x^2 \end{gathered}[/tex]Simplify the expression
[tex]A=36\pi\cdot x^2[/tex]The expression for the surface area of a sphere of radius 3x cm is:
[tex]A=36\cdot\pi\cdot x^2[/tex]Parker offers to pay for 5 of his friends to play laser tag, but 3 of them don't want to play. If laser tag costs $6 per person, how much will Parker spend on his friends? Choose the correct expression and solution to this problem. O A. The expression is 5(6 - 3). Parker will spend $10. B. The expression is 6.5 - 3. Parker will spend $27
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Expression: 6 (5-3) (option C)
Parker will spend $12
Explanation:
number of friends = 5
number of friends that don't play laser tag = 3
The cost of laser tag per person = $6
Amount Parker spend on his friends = 6 (5-3)
Expression: 6 (5-3)
Amount Parker spend on his friends = 6 (5-3) = 6(2)
Parker will spend $12
Find the equation of the line with the given properties. Sketch the graph of the line. Passes through (1, -6) and (8,3)
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A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
If we evaluate our points on this form, we're going to have a linear system where the solutions are those coefficients.
[tex]\begin{cases}3=8m+b \\ -6=m+b\end{cases}[/tex]If we subtract the second equation from the first, we're going to have a new equation only for the slope.
[tex]\begin{gathered} 3-(-6)=8m+b-(m+b) \\ 3+6=8m+b-m-b \\ 9=7m \\ m=\frac{9}{7} \end{gathered}[/tex]Now that we have the slope, we can use any of the equations to find the b value.
[tex]\begin{gathered} -6=(\frac{9}{7})+b \\ -6-\frac{9}{7}=b \\ b=-\frac{51}{7} \end{gathered}[/tex]Then, our line equation is
[tex]y=\frac{9}{7}x-\frac{51}{7}[/tex]And this is the graph
what is the area of a triangle with a base of 5ft and a height of 8.4ft?
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To answer this question, we need to remember the formula for finding the area of a triangle:
[tex]A_{\text{triangle}}=\frac{b\cdot h}{2}[/tex]Where
• b is the base of the triangle
,• h is the height of the triangle
Then, we have that:
b = 5ft
h = 8.4ft
Then, we have:
[tex]A_{\text{triangle}}=\frac{5ft\cdot8.4ft}{2}=\frac{42ft^2}{2}\Rightarrow A_{triangle}=21ft^2[/tex]Therefore, the area of this triangle is equal to 21 sq. feet.
The Reyes family is going to the mall. When they leave home,
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What is the problem about?
Average speed
What information is given?
Starting odometer reading, ending odometer reading, time taken
What do you need to find?
The average speed of the car
An odometer measures the distance traveled by a wheeled vehicle
The starting odometer reading was 54,362 miles
The ending odometer reading was 54,372 miles
It took 15 minutes to get to the mall
Step 1: Find how far Reyes traveled in 15 minutes
54372 - 54362 = 10 miles
At this speed, the car will travel 10 miles in 15 minutes
Step 2: How far the Reyes would travel in 60 minutes?
The Reyes would travel 40 miles in 60 minutes
The sum of two numbers is 35. The larger number is one less than three times the smaller number. Let represent the larger number. Let represent the smaller number. Write a system of equations to represent this situation. What are the two numbers?
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Explanation
To solve the question we will have to set up a simultaneous equation
If x represents the larger number
y represents the smaller number, then
The sum of the two numbers is 35
[tex]Equation\text{ 1: x+y=35}[/tex]The larger number is one less than three times the smaller number.
[tex]Equation\text{ 2: }x=3y-1[/tex]So, we will solve the equation using the substitution method
Thus, we will substitute x = 3y -1 into equation 1
[tex]\begin{gathered} 3y-1+y=35 \\ 3y+y-1=35 \\ 4y-1=35 \\ 4y=35+1 \\ 4y=36 \\ \\ y=\frac{36}{4} \\ \\ y=9 \end{gathered}[/tex]The smaller number is 9
The larger number will be
[tex]\begin{gathered} x+y=35 \\ x=35-y \\ x=35-9 \\ x=26 \end{gathered}[/tex]The larger number is 26
The answers are 9 and 26
A basketball team has 13 Active players, in how many ways can 5 players be selected to start the game??
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Answer:
1287
Explanation:
The number of distinct ways n objects can b selected from N total objects is given by
[tex]\frac{N!}{n!(N-n)!}[/tex]Now in our case, we have a total of 13 basketball players. N = 13 and 5 players to choose n = 5. Therefore, the above formula gives
[tex]\frac{13!}{5!(13-5)!}[/tex][tex]-\frac{13!}{5!8!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5!\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=1287[/tex]Hence, there are 1287 ways 5 different players can be selected from 13 players.
Solve the triangle: Q=60", B = 60", y = 60". If it is not possible, say so.a= 1, b = 1,0 = 1a== 13,6 = 13,0 = 3a = 100,6 = 100,c = 100This triangle is not solvable.
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Solution:
this triangle is not solvable because to solve this triangle we need one of the sides to find the missing sides.
Please help ASAP *image imported*
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Hello, I need some assistance with this homework question please for precalculusHW Q32
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for a science project Miranda will monitor the growth of two different plants, plant 1 and plant 2. at the start of the project plant 1 is 18 I'm tall and plant 2 is 4cm tall. plant 1 is expected to grow at a rate of 3 I'm per week.part a: what is the solution to the systems of equations in Mirandas graph? part b: what is the meaning of the solution to the systems of equations in the context of Miranda plant growth?part c: give a description of what the graph shows should happen with the plants growth before and after the point of intersection.
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The lines in the graph represent the growth rate of two plants, the height is on the y-axis and the time is on the x-axis.
a)
If the plants growth represent an equation system, the solution of said system will be the point where both lines intersect. This point is arround x=7 weeks and y=39 centimeters, you can expres it as a ordered pair (7,39)
b)
This means that by the 7nth week both plants were 39 centimeters tall.
c)
Looking at the graph, the line corresponding to plant 2 is more inclined than the line of plant 1, this means that the growth rate (slope) of plant 2 is greater than the growth rate of plant 1.
The second plant grows faster than the first one.
Total blood cholesterol level was measured for each of 10 adults. Here are the 10 measurements (in mg/dL).176, 251, 247, 262, 150, 214, 192, 194, 154, 255Send data to calculator(a) What is the mean of this data set? If your answer is not aninteger, round your answer to one decimal place.00(b) What is the median of this data set? If your answer is notan integer, round your answer to one decimal place.(c) How many modes does the data set have, and what aretheir values? Indicate the number of modes by clicking in theappropriate circle, and then indicate the value(s) of themode(s), if applicable.zero modesone mode:two modes: andXS
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a) 209.5mg/dL
b) 204mg/dL
c) zero modes
Explanations:Mean is also known as average of a dataset. Given the data expressed below;
[tex]Mean=\frac{sum\text{ of data}}{sample\text{ size}}[/tex]Given the following parameters
Sum of data = 176 + 251 + 247 + 262 + 150 + 214 + 192 + 194 + 154 + 255
Sum of data = 2095
Sample size = 10 (Total measurement)
Determine the mean of the data
[tex]\begin{gathered} Mean=\frac{2095}{10} \\ Mean=209.5 \end{gathered}[/tex]Therefore the mean of the data is 209.5mg/dL
b) The median of the dataset is the value in the middle after rearrangement. On rearranging in ascending order;
150, 154, 176,192, (194, 214), 247, 251, 255, 262
The two values at the middle are 194 and 214.
[tex]\begin{gathered} Median=\frac{194+214}{2} \\ Median=\frac{408}{2} \\ Median=204 \end{gathered}[/tex]c) The mode of the data is the value that occur the most in the dataset. SInce all the data only appear once in the dataset, hence there are ZERO MODES
1.Find the quotient of 1/2and 3/4.2. Divide 4by2/33.If 5/9is divided by3, what is the quotient4. Mrs. Dolentebuys 5 1/2kilograms of rice. If she cooks 1/4kilogram for every meal, how many meals will it last?5.Marita needs 2/3meter of lace for each pillowcaseshe makes. How many pillowcasescan she make with 7 1 3meters of lace
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1) We can find the quotient between two fractions by multiplying the first one by the reciprocal of the second one this way:
[tex]\frac{\frac{1}{2}}{\frac{3}{4}}=\frac{1}{2}\times\frac{4}{3}=\frac{4}{6}=\frac{2}{3}[/tex]2) Let's now divide 4 by 2/3 following the same principle:
[tex]\frac{4}{\frac{2}{3}}=4\times\frac{3}{2}=\frac{12}{2}=6[/tex]Notice that we have simplified as well as the previous item (1).
3) Proceeding with that we have:
[tex]\frac{\frac{5}{9}}{3}=\frac{5}{9}\times\frac{1}{3}=\frac{5}{27}[/tex]4) To find this out, we need to convert that Mixed Number to Improper Fraction:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{2\times5+1}{2}=\frac{11}{2} \\ \frac{\frac{11}{2}}{\frac{1}{4}}=\frac{11}{2}\times4=\frac{44}{2}=22 \end{gathered}[/tex]We kept the denominator then multiplied it by the whole number and added it to 1. So it will last 22 meals.
5) To find it out we are going to divide 7 1/3 by 2/3 meter, after converting that Mixe Number into an Improper Fraction:
[tex]\begin{gathered} 7\frac{1}{3}=\frac{3\times7+1}{3}=\frac{22}{3} \\ \frac{\frac{22}{3}}{\frac{2}{3}}=\frac{22}{3}\times\frac{3}{2}=\frac{66}{6}=11 \end{gathered}[/tex]Notice, that we have used the same procedure to convert from Mixed Numbers to an Improper fraction. Marita can make 11 pillowcases.
And those are the answers.
41. Supermarket discount stores, and drugstores use a measure called sales per linear foot in deciding how much shelf space to allot for different items. To calculate this measure, divide the gross sales of an item by the number of linear feet of shelf space that the item occupies. Consider the following figures for two brands of vitamins: 
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I need help fast thanks it looks kinda hard and I can’t figure it out
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Looking at the figure, we see that there are 6 identical squares of side 26 yd.
We know that the area of a square of side L can be calculated using the formula:
[tex]A=L^2[/tex]Now, if there are 6 squares, the total area is:
[tex]A_{\text{Total}}=6\cdot L^2[/tex]From the problem, L = 26 yd, then:
[tex]\begin{gathered} A_{\text{total}}=6\cdot26^2 \\ \therefore A_{Total}=4056yd^2 \end{gathered}[/tex]A radar gun measured the speed of a baseball at 103 miles per hour. If the baseball was actually going 102.8 miles per hour, what was the percent error in this measurement? Round to the nearest hundredth percent
Answers
Answer
Percent Error = 0.195%
Explanation
Percent error is given as
[tex]\text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent}[/tex]Error = | (Incorrect value) - (True value) |
Incorrect value = 103 miles per hour
True value = 102.8 miles per hour
Error = | (Incorrect value) - (True value) |
Error = | 103 - 102.8 |
Error = 0.2 miles per hour
[tex]\begin{gathered} \text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent} \\ \text{Percent Error = }\frac{0.2}{102.8}\times100\text{ percent} \\ \text{Percent Error = 0.195 percent} \end{gathered}[/tex]
Hope this Helps!!!
If a board 9 feet 6 inches in length is cut into 2 equal parts, what will be the length of each part?
5 feet 2 inches
4 feet 8 inches
4 feet 5 inches
4 feet 9 inches
3 feet 8 inches
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Answer:
4 feet and 9 inches
Step-by-step explanation:
First, we shall convert 9 feet and 6 inches into just inches.
9 x 12 = 108
108 + 6 = 114 inches.
114 divided by 2 = 57 inches.
Then, we divide 57 by 12:
57 divided by 12 = 4.75.
So, we have 4 feet.
0.75 x 12 = 9 inches.
In conclusion, we have 4 feet and 9 inches.
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Describe the transformations made on this function:(stretch/compression, reflect, left/right, up/down)
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The function we have is:
[tex]f(x)=\frac{1}{2}(x-7)^3+6[/tex]Since this is a cubic function, we start with the parent cubic function (the simplest form of the cubic function):
[tex]f(x)=x^3[/tex]And compare it to the given function.
The first thing we can note is that there was a subtraction of 7 to the value of x:
[tex]x\longrightarrow x-7[/tex]When we add a number to the x value, the graph moves to the left, and when we subtract a number to the x value, the graph moves to the right.
So the first transformation is moving to the right 7 units.
Next, we have that there was +6 added to the expression --> When you add a number to the function, the graph moves up, and when you subtract a number to the function, the graph moves down.
In this case, since we added a constant value of 6, the graph is translated 6 units up.
The second transformation is moving up 6 units.
Finally, let's analyze the effect that the 1/2 has on the function.
We can compress or stretch the graph of a function by multiplying the x by a constant (a number). If the number of between 0 and 1, there is a stretch, and if the number is greater than 1 there is compression.
In this case, the number next to the x is:
[tex]\frac{1}{2}=0.5[/tex]Since the number is between 0 and 1 there is a stretch of the function.
In summary:
Answer:
Translation of 7 units to the right
Translation of 6 units up
Stretch of the function of 0.5