![daytonalive7193](/avatars/27036.jpg)
daytonalive7193
03.12.2020 •
Mathematics
Please discuss the relationship between the value of "a" in a quadratic function [y = a(x - h)2 + k or y = ax2 + bx + c] and the distance the focus is from the vertex. Please give examples to support your conclusion. Please Help!
Solved
Show answers
More tips
- L Leisure and Entertainment Choosing the Right Books to Read: Tips and Recommendations...
- L Leisure and Entertainment What can be considered an antique: defining and valuing old objects...
- B Business and Finance How to Open an Online Store? A Detailed Guide for Beginners...
- C Computers and Internet Log-in: what is it and why do you need it?...
- C Computers and Internet What is the Meaning of lol and How Did it Become Popular?...
- C Computers and Internet Clearing Cache: How to Speed Up Your Browser...
- H Health and Medicine How to Help Men Gain Weight?...
- F Family and Home How to Build a Strong Relationship with Your Child: Tips for Effective Communication...
- L Legal consultation Juvenile Justice: Who Needs It?...
- F Food and Cooking What age is appropriate for giving your child cocoa?...
Answers on questions: Mathematics
- M Mathematics Do you believe that the tax brackets should have smaller range? why or why not?...
- M Mathematics Plz answer yes or no...
- M Mathematics Find a third degree polynomial having only real coefficients, 2 and -2i are zeros and f(3)=-15...
- M Mathematics Find the slope of the graph of the linear function, f, if f(3) = 6 and f(-2) = -4....
- B Biology Calculate the percentage of mass remaining for samples d, e, and f to the nearest tenth of a percent. record the percent of mass remaining in table a of your student guide. what...
- B Biology What needs to happen for a species to form...
- E English (2) Even though the school doesn’t belong to me---it belongs to the whole district it feels like my own home. (3) I clean it, take care of it, and love it. 1. What is the best...
Ответ:
The given equations are;
y = a·(x - h)² + k or y = a·x² + b·x + c
We have;
(x - h)² = 4·p·(y - k),
Where;
(h, k) are the x, and y coordinates of the vertex
p = The distance from the focus to vertex distance;
Comparing, we have;
y - k = a·(x - h)²
(y - k)/a = (x - h)²
(x - h)² = 4·p·(y - k)
4·p·(y - k) = (x - h)²
∴ 4·p = 1/a
p = 1/(4·a)
Therefore, the focus to vertex distance inversely proportional to the value of a
The distance of every point on the parabola is equidistant from the directrix and the focus
Therefore, the equation of the directrix is y = k - p
For example, we have;
y = 2·x² + 3·x + 1
h = -b/2a = -3/4
k = (4ac - b²)/4a = (4×2×1 - 3²)/(4×2) = -1/8
The coordinate of the focus is (h, k + p) = (-3/4, -1/8 + 1/8) = (-3/4, 0)
The directrix, y = k - p = -1/8 - 1/8 = -1/4
For a point x = 2, we have, y = 2·2² + 3·2 + 1 = 15
The coordinate of the point is (2, 15)
The distance of the point from the directrix = 15 - (-1/4) = 15 + 1/4 = 15.25
The distance of the point from the focus is √((2 - (-3/4))² + (15 - 0)²) = 15.25
Therefore, all points on the parabola have equal distances from the focus and the directrix
Step-by-step explanation:
Ответ:
1/8
Step-by-step explanation:
white shirt= 1/4
tan pants= 1/2
white shirt and tan pants = 1/8