1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
quester [9]
3 years ago
5

Find the vertex, focus, directrix, and focal width of the parabola. (5 points)

Mathematics
1 answer:
Anarel [89]3 years ago
8 0

\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf -\cfrac{1}{20}x^2=y\implies \cfrac{x^2}{-20}=y\implies x^2=-20y\implies (x-0)^2=-20(y-0) \\\\\\ (x-\stackrel{h}{0})^2=4(\stackrel{p}{-5})(y-\stackrel{k}{0})

something noteworthy is that the squared variable is the "x", thus the parabola is a vertical one, the "p" value is negative, so is opening downwards, and the h,k is pretty much the origin,

vertex is at (0,0)

the focus point is "p" or 5 units down from there, namely at (0, -5)

the directrix is "p" units on the opposite direction, up, namely at y = 5

the focal width, well, |4p| is pretty much the focal width, in this  case, is simply yeap, you guessed it, 20.

You might be interested in
The American novel began to develop in the eighteenth century. a. True b. False
Galina-37 [17]
The answer would be true.
5 0
3 years ago
Read 2 more answers
Can someone help me understand squares,cubes,and roots with example problems please
erastova [34]

when someone says a number squared or cubed, or to the certain power, it means how many times you multiply the base number by itself that many times, for example

2²= 2 * 2

or 9³ = 9 x 9 x 9

a square root or cube root, is a harder to understand, but still somewhat simple, it basically means how many what number squared or cubed equals this number.

so for example the square root of 9 = 3 because 3 x 3=9

or cube roots for example ∛125= 5 because 5 x 5 x 5

So here is an example one for you. √81.

4 0
3 years ago
Mr de guzman bought 7 1/2 of meat.He used 2 3/4 for afritada,3 1/8 kg for menudo and the rest for pochero.How many kilograms of
nasty-shy [4]

Answer:

hola puto

Step-by-step explanation:

bggyyhh yyesws kihtwrqas bts23e4gyhun

7 0
3 years ago
Three times one number added to five times another number is 54. The second number is two less than the first. Use a system of e
worty [1.4K]

Answer:

8 and 6

Step-by-step explanation:

If you use x for the first number, and y for the second, you get equations of 3x+5y=54 and x-2=y.

You can substitute the second equation into the first one to solve it. This gives 3x+5(x-2)=54.

The brackets can be expanded to 3x+5x-10=54. Collecting like terms makes it 8x-10=54.

Next, we add 10 to both sides. This gives 8x=64.

From there, we isolate the x by dividing both sides by 8, giving x=8.

To work out the second number, we can sub 8 for x in either equation (I'm using the second one as it's simpler).

This comes to y=8-2, therefore y=6.

**This content is simultaneous equations, which you may wish to revise. I'm always happy to help!

3 0
3 years ago
Cuánto es (-12) - 21 = <br>Explicación del pq da a ese resultado, por favor.​
Gelneren [198K]

Answer:

the answer is -33 srry couldn't explain :(

7 0
3 years ago
Read 2 more answers
Other questions:
  • Please help! i’m struggling in math so much!
    10·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%7B40a%7D%5E%7B2%7D%20%20%2B%2020a%20-%2030%20%3D%20%28%20-%201%29%28%20%20%7B15a%7D%5E%7B3
    10·1 answer
  • A bag contains both black and red marbles. The ratio of black to red marbles is 3:4.
    12·1 answer
  • Thomas bought his whole family hot dogs and popcorn at the baseball game. He bought 60 items. He bought 3 hot dogs and and 8 pop
    11·2 answers
  • A point has the coordinates (0,k).
    11·1 answer
  • URGENT WILL GIVE BRAINLIEST PLZ HELP
    6·1 answer
  • Underwood Farms had 242 pumkins at the start of November . 12 visitors brought 2 pumkins wach by November 10th. How many pumkind
    9·1 answer
  • Find the volume of a rectangular prism with the dimensions:
    14·2 answers
  • 3) Solve the problem.
    5·2 answers
  • Maggie and her friends are each able to recruit a certain number of people each year to sample a product. The number of people p
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!