Juicebox18
27.02.2020 •
Mathematics
TIME REMAINING
58:52
What is the equation of the graphed line written in standard
form?
2x - y= 4
- v=4
y=2x-4
0 v= 1 / 2 x - 4
Solved
Show answers
More tips
- H Health and Medicine 10 Simple and Effective Tips on How to Lose Weight in a Week...
- C Computers and Internet Where did torrents.ru move to?...
- B Business and Finance Understanding Cash Flow: What It Is and How It Works...
- C Computers and Internet What Are Peers and Seeds in Torrenting?...
- H Health and Medicine 10 Simple Techniques on How to Boost Your Mood...
- G Goods and services How to Choose the Right High Chair for Your Baby?...
- S Style and Beauty Learn how to tie a keffiyeh on your head like a pro...
- S Style and Beauty How to braid friendship bracelets?...
Answers on questions: Mathematics
- M Mathematics How do i solve the next question? 8 (x + 6) = 72...
- M Mathematics What is the measure of the central angle of a circle with radius 15 ft that intercepts a 10 ft arc? Use 3.14 for pi Round the answer to the hundredths place. Enter your answer...
- M Mathematics Which equation represents the line that passes through the point (3, –1) and is perpendicular to the graph of x + 4y = 10?...
- M Mathematics If – 7 x -3 and 24 y 31, what is the largest possible value for X – y? A) -34 B) -31 С) -27 D) 28 E) 31...
- M Mathematics Here... it says its to short so im still typing...
- M Mathematics Can some help me i will mark you as Brainliest dont answer in a file its the one with the box around it...
- M Mathematics Please help. I need which letters to click...
- M Mathematics 3/8+1/8= Find the sum or difference...
- M Mathematics Provide an appropriate response. A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner suspects that it is less than that. She...
- M Mathematics COLOR OF SHIRT NUMBER SOLD black 24 blue 12 red 20 yellow 6 The table above shows the number of T-shirts sold at a booth last week. The vendor orders shirts for two weeks...
Ответ:
See diagram, attached.
Part A: Equation of the directrix is y= -2
Part B: point of intersection A of directrix & line of symmetry A(6,-2)
Part C: y = (1/12) (x-6)^2+1
or on simplifying
12y = x^2 -12x +48
(Note: given instructions omitted the +k term.)
part D: The parabola opens upwards becaus p>0.
Part E: The value of p is the difference of y coordinates of F minus the y-coordinate of A, all divided by 2, which is positive.
Part F: p = (4 - (-2))/2 = +3
Part G: y = (1/12)(x-6)^2 + 1
Part H: See attached diagram below
Part I : y = (1/12) (x-6)^2 + 1 where h=6, k=1, or V(6,1).
It fits with the given formula, provided we include the +k term.
Step-by-step explanation:
The vertex form of the equation of a vertical parabola is given by y= 1/4p(x-h)^2 , 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 the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.
Part A: Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line? (y=-2)
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? A(6,-2)
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.
We know that the equation in vertex form is
y = (1/(4p)(x-h)^2+k where V(h,k) are the coordinates of the vertex.
From points F and A, we know that the distance from directrix to focus is 6.
Therefore p=3.
The vertex, V(h,k) is located at the mid point between the segment joining the directrix and the focus, namely A & K, which has coordinates V(6,1), thus h=6, k=1.
The equation of the parabola is therefore
y = (1/(4p) * (x-h)^2 +k) = (1/(4*3))(x-6)^2 +1 = (1/12) (x-6)^2+1
(note: given instructions omitted the +k term.)
Simplifying
12y = x^2 -12x +36+12
12y = x^2 -12x +48
Part D: Which way will the parabola open? Explain.
The parabola opens upwards becaus p>0.
Part E: How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
The value of p is the difference of y coordinates of F minus the y-coordinate of A, all divided by 2, which is positive.
Part F: What is the value of p for your parabola?
p = (4 - (-2))/2 = +3
Part G: Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
y = (1/12)(x-6)^2 + 1
Part H: Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
See attached diagram 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.
1.33...x^2 - 16x -16y = -64
Multiply all by 3/4
x^2-12x-12y=-48
rearrange
12y = x^2-12x+36 +12
Factor
12y = (x-6)^2 + 12
Divide by 12 all through
y = (1/12) (x-6)^2 + 1 where h=6, k=1, or V(6,1).
It fits with the given formula, provided we include the +k term.