The vertex form of the equation of a horizontal parabola is given by x=1/4p(y-k)2+h , where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use GeoGebra to create a horizontal parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below.
Part A
Mark the focus of the parabola you are going to create at F(-5, 2). Draw a vertical line that is 8 units to the right of the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part B
Construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola?
Part C
Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.
Part D
Which way will the parabola open? Explain.
Part E
How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
Part F
What is the value of p for your parabola?
Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
Part H
Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
Part I
Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work
Part J
To practice writing the equations of horizontal parabolas, write the equations of these two parabolas in vertex form:
focus at (4, 3), and directrix x = 2
focus at (2, -1), and directrix x = 8
Answers
Answer:
A. x = 3
B. A = (3, 2)
C. V = (-1, 2)
D. Left
E. See below.
F. p = -4
[tex]\textsf{G.} \quad x=-\dfrac{1}{16}(y-2)^2-1[/tex]
H. See attachment.
[tex]\textsf{J.} \quad x=\dfrac{1}{4}(y-3)^2+3[/tex]
[tex]x=-\dfrac{1}{12}(y+1)^2+5[/tex]
Step-by-step explanation:
Part AThe given focus of the parabola is F (-5, 2).
The equation for a vertical line is x = a.
Therefore, a vertical line that is 8 units to the right of the focus is:
[tex]\implies x=-5+8=3[/tex]
Therefore:
Directrix: x = 3Part BA line that is perpendicular to the directrix is a horizontal line.
The equation for a horizontal line is y = a.
As the horizontal line passes through the focus:
Axis of symmetry: y = 2The point of intersection, A, of the axis of symmetry and the directrix is:
(3, 2)Part CThe vertex of the parabola is the point that is halfway between the focus and the directrix.
Therefore:
Vertex = (-1, 2)Part DThe parabola will open sideways as the axis of symmetry is horizontal.
As a parabola never touches its directrix, this parabola will open to the left.
Part EThe absolute value of p is the distance between the vertex and the focus, and the distance between the vertex and the directrix.
For a sideways parabola, if p > 0 the parabola opens to the right, and if p < 0 the parabola opens to the left.
Part FSince the focus and directrix are 8 units apart, and the parabola opens to the left:
p = -4Part GVertex form of a sideways parabola:
[tex]\boxed{x=\dfrac{1}{4p}(y-k)^2+h}[/tex]
Given:
Vertex = (-1, 2) ⇒ h = -1, k = 2p = -4Substitute the values into the formula:
[tex]\implies x=-\dfrac{1}{16}(y-2)^2-1[/tex]
Part HSee attachment.
Part IRearrange the equation of the parabola shown in the attachment:
[tex]y^2+16x-4y=-20[/tex]
[tex]\implies 16x=-y^2+4y-20[/tex]
[tex]\implies 16x=-(y^2-4y+4)-16[/tex]
[tex]\implies 16x=-(y-2)^2-16[/tex]
[tex]\implies x=-\dfrac{1}{16}(y-2)^2-1[/tex]
This matches the equation in vertex form in part G.
Part JGiven:
Focus = (4, 3)Directrix: x = 2Therefore:
Vertex = ((4+2)/2, 3) = (3, 3)Parabola opens to the right, so p > 0.p = |4 - 3| = 1Therefore, the equation of the parabola with the given parameters is:
[tex]\boxed{x=\dfrac{1}{4}(y-3)^2+3}[/tex]
Given:
Focus = (2, -1)Directrix: x = 8Therefore:
Vertex = ((8+2)/2, -1) = (5, -1)Parabola opens to the left, so p < 0.p = -|2 - 5| = -3Therefore, the equation of the parabola with the given parameters is:
[tex]\boxed{x=-\dfrac{1}{12}(y+1)^2+5}[/tex]
Related Questions
PLEASE HELP ME.!! I WILL GIVE BRAIN LIST
Which graph shows the image of ΔABC after a rotation about the origin?
Answers
Answer: Choice B
Answer:
B
Step-by-step explanation:
A is a reflection across the y-axis.
B is the result of a rotation around the origin either by 90° counterclockwise, or by 270° clockwise.
C is a reflection across the x-axis.
D is a translation (shift) by -5 to the left.
hi! Can someone please help me out? Thank you so much :) I’ll give brainly. Question is in image
Answers
Answer:
d) 189.3 in²
Step-by-step explanation:
Area of rectangle is,
→ w × l
→ 10 × 15
→ 150 in²
Area of semi circle is,
→ (1/2)πr²
→ (1/2) × 3.14 × (5)²
→ 1.57 × 25
→ 39.3 in²
Now the total area will be,
→ 150 + 39
→ 189.3 in²
Thus, total area is 189.3 in².
{ | ∈ and 3 ≤ < 9} ROOSTER MODE
Answers
The rooster form of the given set is {3, 4, 5, 6, 7, 8}
What is the rooster form of set?The contents of a set can be described by listing the elements of the set, separated by commas, inside a set of curly brackets. This way of describing a set is called roster form.
Given a set, {I ∈ ≤3<9}
Converting in rooster form, {3, 4, 5, 6, 7, 8}
Hence, The rooster form of the given set is {3, 4, 5, 6, 7, 8}
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Choose an equation in slope-intercept form for the line that passes through (0,7) and is parallel to the y=4x-19
a. y= (1/4)x - 7
b. y= (1/4)x + 9
c. y = 4x + 3
d. y = 4x + 7
Answers
Answer:
Step-by-step explanation:
You dont even need to look at the slope. For it to pass through (0,7) answer d with the +7 at the end is the only right answer
your welcome
D
Keiko estimated that it would take her 18 hours to build a shed for her 12.5 backyard. It only took her hours. What is the percent error of her estimate relative to the time it actually took?
Answers
The percent error of her estimate relative to the time it actually took is approximately 5.9%
What is the percent error?Estimated time to construct the shed = 18 hoursActual time taken to build the shed = 17 hoursError = Estimated time to construct the shed - Actual time taken to build the shed
= 18 hours - 17 hours
= 1 hour
Percent error = error / actual time × 100
= 1/17 × 100
= 0.058823529411764 × 100
= 5.882352941176470
Approximately,
5.9%
Consequently, the percent error of Keiko estimation and actual time is 5.9%
Complete question:
Keiko estimated that it would take her 18 hours to build a shed for her 12.5 backyard. It only took her 17 hours. What is the percent error of her estimate relative to the time it actually took?
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A line has a slope of 1 and passes through the point (-2, 8). What is its equation in slope-intercept form?
Answers
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 1}(x-\stackrel{x_1}{(-2)}) \implies y -8= 1 (x +2) \\\\\\ y-8=x+2\implies {\Large \begin{array}{llll} y=x+10 \end{array}}[/tex]
Answer: The answer is y=x+10
If angle 1 is 25 degrees in the parallelogram pictured above, what is angle 2
if q is 1x+ 10 and AC is 7x+8 what is the length of AC? Round your answer to the nearest hundredth
Answers
Applying the properties of a parallelogram:
1. Length of AC = 24.8 units
2. x = 1
What are the Properties of a Parallelogram?Some properties of parallelogram we need to recall in order to solve the problem given are:
They have two pair of sides that are parallel to each other and also of the same length.They have two diagonals that bisect each other into equal halves.1. q = 1x + 10
AC = 7x + 8
Therefore:
q = 1/2(AC) [based on the property of a parallelogram]
Substitute
x + 10 = 1/2(7x + 8)
Solve for x
2(x + 10) = 7x + 8
2x + 20 = 7x + 8
2x - 7x = -20 + 8
-5x = -12
x = -12/-5
x = 2.4
Length of AC = 7x + 8 = 7(2.4) + 8
Length of AC = 24.8 units
2. x + 8 = 7x + 2 [based on the property of a parallelogram]
x - 7x = -8 + 2
-6x = -6
-6x/-6 = -6/-6
x = 1
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PLEASE HELP ASAP 20 POINTS
Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 22.75°. What is the measure of ∠P?
22.75°
78.625°
134.5°
157.25°
Answers
Answer:
<P = 78.625°
Step-by-step explanation:
All of the angles in a triangle add up to 180.
<R + <Q + <P = 180
We can use x for <P and <Q, as they represent the same value because they are congruent.
<R + x + x = 180
Now, we want to substitute known values in and work backwards to find out what angle <P and <Q are.
2x + <R = 180
Put 22.75 in for <R.
2x + 22.75 = 180
Subtract on both sides.
2x = 157.25
Divide 2 on both sides to isolate x
x = 78.625
Since x represents <P and <Q, that means they are both 78.625 degrees each.
<P = 78.625
Find the distance between (−7, 2) and (−6, 3). Round your answer to the nearest tenth.
Answers
Answer:
[tex]\huge\boxed{\sf D=1.4 \ units}[/tex]
Step-by-step explanation:
Points:[tex](x_1,y_1)=(-7,2)[/tex][tex](x_2,y_2)=(-6,3)[/tex]Distance Formula:Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Put the above points in the formula.
[tex]D=\sqrt{(-6-(-7))^2+(3-2)^2} \\\\D=\sqrt{(-6+7)^2+1^2} \\\\D=\sqrt{1^2+1} \\\\D=\sqrt{1+1} \\\\D=\sqrt{2} \\\\D=1.4 \ units\\\\\rule[225]{225}{2}[/tex]
HELP PLEASE this is urgent
Answers
Answer:
10.5 cm
Step-by-step explanation:
YZ corresponds to TU
YZ:TU = 9:3 = 3:1
XY corresponds to ST
ST = 3.5 cm
XY:ST = 3:1
XY/ST = 3/1
XY/3.5 cm = 3
XY = 10.5 cm
Step by step
Line up your known sides
TU and ZY are similar
The dilation rate is small to large x3 ratio
(9/3) therefore
ST to TY is also rate of x3
ST = 3.5 x 3 = 10.5cm
The value of a brand new car depreciates 10% when leaving the agency and another 5% after the first year of use. After one year of use, the value of a certain automobile is $51,300.00. Which of the following mathematical expressions correctly represent the value (x) of this automobile zero km? x times open parentheses 0 comma 10 plus 0 comma 05 close parentheses equals 51300 double right arrow x equals 342000 x times open parentheses 0 comma 90 plus 0 comma 95 close parentheses equals 51300 double right arrow x equals 26308 x equals 51300 plus 51300 over 10 plus 51300 over 5 double right arrow equals 66690 x equals 51300 minus open parentheses 51300 over 10 plus 51300 over 5 close double right arrow x equals 35910 x times 0 comma 90 times 0 point 95 equals 51300 double right arrow x equals 60000
Answers
The value of the car zero km is given by the expression x = 60000.
LET ME EXPLAIN SOMETHING:
An algebraic expression is one that has several operations between numbers and letters (unknowns): addition, multiplication, subtraction, division, potentiation, rooting, etc.
LET'S GO TO THE SOLUTION:
Let x be the initial value of the car, we know that it depreciates 10% when leaving the agency and another 5% after one year. If the value of this car is $51,300.00 after 1 year, we will have to:
When you leave the agency, your value decreases by 10%:
x·(100% - 10)% = 90% of x = 0.9xAfter a year, its value decreases by 5%:
0.9x·(100% - 5)% = 95% of 0.9x = 0.855x0.855x = 51300
x = 60000
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https://brainly.com/question/953809In a class, the ratio of girls to boys is 2:3. There are 12 boys in the class. How many women are in the class?
Group of answer choices
1. 13
2. 18
3. 8
4. 11
Answers
Answer:
8
Step-by-step explanation:
Because we multiply 4 by both sides
2 times 4 is 8 for girls
4 times 3 is 12 for boys
So it asked for girls and 4 times 2 is 8
So the answer is 8
8 women are in the class.
The midpoint of AB is M (3, -1). If the coordinates of A are (8, 4), what are the coordinates of B?
Answers
solve for U
3u − –2 = 8
U=
Answers
3(2) - -2 =8
3 times 2 equals 6.
And 6 plus 2 equals 8.
When a subtraction symbol is in front of a negative number you add.
+*+=+
+*-= -
-*- = +
-*+= -
So back to the Question
3*2= 6
6+2= 8
U=2
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
From the solution to the given inequality, the correction representations are -6x + 15 < 10 - 5x and a number line from -3 to 7, with an open circle at 5 and an arrow pointing to the right.
Solving Linear InequalitiesFrom the question, we are to determine the correct representations of the given inequality
The given inequality is
-3(2x - 5) < 5(2 - x)
To determine the correct representation, we will solve the inequality
Solving the inequality
-3(2x - 5) < 5(2 - x)
Clear the parentheses by applying the distributive property
-6x + 15 < 10 - 5x
Add 6x to both sides
-6x + 6x + 15 < 10 - 5x + 6x
15 < 10 + x
Subtract 10 from both sides
15 - 10 < 10 - 10 + x
5 < x
Therefore,
x > 5
Hence, the correction representations are -6x + 15 < 10 - 5x and the number for x > 5
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If a firm sold some inventory on credit as opposed to cash, there is no reason to think that either its current or quick ratio would change. a
Answers
The given statement would be "false".
What is the quick ratio?A quick ratio compares the company's most liquid assets to a short-term commitment. The quick ratio is computed by adding the cash and equivalents of the firm to its short-term investments and account receivable. Divide the figure by the firm's existing liabilities.
As per the question, there is no reason to believe that if a company sold any goods on credit rather than cash, its current or quick ratio would change that would be false.
Thus, the given statement would be "false".
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The question seems to be incomplete the correct question would be:
Find the statement true or false.
If a firm sold some inventory on credit as opposed to cash, there is no reason to think that either its current or quick ratio would change. (T/F)
Find the values of x and y.
x + 2 = 3y
Answers
31 MULTIPLE CHOICE which of the following is not possible geometry
Answers
Answer:
? where are the questions i will edit when answer arrive.
Step-by-step explanation:
Last year, 769 of the 1,307 residents in a small town owned more than one vehicle.
Use this historical data to find the probability that a randomly selected resident in this small town owns more than one vehicle.
Answers
Around 58 percent
7x - 10y = 28
7x - 3y = 28
Answers
Answer:
(4, 0)
Step-by-step explanation:
7x - 10y = 28
7x - 3y = 28
------------------
(7x - 10y = 28) × -1
-7x + 10y = -28
--------------------------
-7x + 10y = -28
7x - 3y = 28
--------------------------
7y = 0
y = 0
7x - 10y = 28
7x - 10(0) = 28
7x = 28
÷7 ÷7
----------------
x = 4
(x, y)
(4, 0)
I hope this helps!
x-intercepts for 7x - 10y = 28:
(4,0)
y-intercepts:
(0, -14/5)
x-intercepts for 7x - 3y = 28:
(4, 0)
y-intercepts:
(0, -28/3)
Step-by-step explanation:I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
If one of the factors from the product of 3 identical factors of a number is 4, what is that number?
Answers
Answer:
64
Step-by-step explanation:
Since one of the 3 identical factors is 4, then the number is 4×4×4, or 4³
mean of 1/3 and - 2/5
Answers
Answer:
-1/30
Step-by-step explanation:
add the two numbers and divide by 2
Question 43 of 50
The graph of an exponential function that is increasing is ƒ(x) = (1/5)x.
False
True
Answers
Answer:
Option: A is the correct answer.
Step-by-step explanation:
Clearly from the graph we could observe that the graph is a decay exponential function as the graph of the function is decreasing with the increasing value of x.
Hence, the rate has to be less than 1.
So, option: B and D are ruled out as they represent a growth exponential function.
Also from the graph given in the question we could observe that when x=0 the value of y is:
y=4
So, the exponential function that is represented by the graph is:
Answer: true
Step-by-step explanation:
A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages.
64, 40, 45, 43, 33, 50, 47, 49, 42, 28, 55, 64, 55, 41, 65.
64, 50, 45, 51, 23, 35, 64, 43, 45, 37, 37, 47, 34, 27, 49,
62, 39, 35, 44, 23, 36, 42, 34, 32, 52.
D
Answers
The required leaves values for the given stems are calculated below.
What is Stem-and-Leaf plot?A plot where every information esteem is parted into a "leaf" (typically the last digit) and a "stem" (different digits). For instance "32" is parted into "3" (stem) and "2" (leaf). The "stem" values are recorded down, and the "leaf" values are recorded close to them.
For example , 42, 34, 48, and so on.
Here 42 and 48 qualities will be written in stem 4 as their most memorable digit is 4, while 2 and 8 will be placed in the leaf side.
Likewise, 3 will be the stem, and 4 will be the leaf for esteem 34.
4| 2, 8
3| 4
According to question:65, 40, 47, 47, 33, 55, 44, 49, 46, 22, 58, 65, 56, 41, 63, 65, 54, 42, 58, 29, 39, 66 , 49, 42, 34, 36, 42, 35, 21, 44, 61, 35, 33, 42, 27, 30, 46, 33, 35, 58.
As given in the question that the stem and Leaves are to be separated by a hyphen.
Stem-and-Leaf plot 6 - 5, 5, 3, 5, 6, 1
5 - 5, 8, 6, 4, 8, 8
4 - 0, 7, 7, 4, 9, 6, 1, 2, 9, 2, 2, 4, 2, 6
3 - 3, 9, 4, 6, 5, 5, 3, 0, 3, 5
2 - 2, 9, 1, 7
As we can see above there are 5 stems, where stem 6 has 6 leaves, stem 5 has 6 leaves, stem 4 has 14 leaves, stem 3 has 10 leaves, and stem 2 has 4 leaves.
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If fx)=1/9x-2, what is f¹(x)?
0 f¹(x)= 9x + 18
0 f¹(x)= 1/9x+ 2
0 f¹(x)= 9x+2
0 f¹(x)= -2x + 1/9
Answers
Answer:
f⁻¹(x)= 9x + 18
Step-by-step explanation:
1. Replace f(x) with x, and x with y: x=1/9y-2
2. Solve for y:
x=1/9y-2
9x=y-18
9x+18=y
3. Replace y in step 2 with f⁻¹(x)
The price of a gallon of unlead gas has risen to $2.88 today. yesterdays price was $2.83. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Hope this helps!
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HELP!! PLS JT WONT TAKE LONG. IS THIS PHOTO CURVE A NORMAL DISTRIBUTION. WHY OR WHY NOT.
Answers
Answer:
no, it isn't symmetrical
Step-by-step explanation:
give me brainliest pls
The following coordinate plane shows three of the vertices of a rectangle. On an 8 by 8 coordinate grid, T is plotted 1 unit right and 4 units up from the origin. P is plotted 6 units right and 2 units up from the origin. Z is plotted 3 units right and 5 units up from the origin. What are the coordinates of Point Z? ( Choose... ) What are the coordinates of Point P? ( Choose... ) Which point has coordinates ( 1 , 4 ) ? Choose... In order to create a rectangle using these points as three of the vertices, what coordinates should be used for the fourth vertex? ( Choose... )
Answers
The coordinates of the points are given as follows:
Point Z: (3,5).Point P: (6,2).Point T has coordinates (1,4).The coordinates of the fourth vertex are of:
(4,1).
What are the ordered pairs?The notation of an ordered pair is given as follows:
(x-coordinate,y-coordinate).
The x-coordinate is the horizontal movement, defined as follows:
Right: positive x-coordinate.Left: negative x-coordinate.The y-coordinate is the vertical movement, defined as follows:
Up: positive y-coordinate.Down: negative y-coordinate.The equivalent sides on a rectangle are congruent, hence the equivalent sides are:
TZ and PM.
Hence the missing coordinate M is:
1 unit down from P, hence y = 2 - 1 = 1.2 units left from P, 6 - 2 = 4.More can be learned about ordered pairs at brainly.com/question/1528681
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-14x - 6 + 8 What is the answer???
Answers
Answer:
The answer is 2-14x or
-12x
Find the surface area
3yd
3yd
8yd
Answers
Answer: 72
Step-by-step explanation: 3 x 3 x 8 = 72
3 x 3 = 9
9 x 8 = 72