Use the given information to write the equation of the parabola.
Vertex: [tex](0,0)[/tex]
Focus: [tex](0,-\dfrac{1}{2})[/tex]
Answers
Answer:
x² = -2y
Step-by-step explanation:
The focus is p away from the vertex, and so is the directrix.
To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.
Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)Vertical parabola [Standard form]: (x – h)² = 4p(y – k)If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).
Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).
For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).
You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).
If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.
Now we can just plug in our known information to derive the equation!
h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →
(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →
x² = -2y.
Also p = 1/4a, if you are wondering.
So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.
Answer:
[tex]\boxed {\boxed {\sf x^2=-2y}}[/tex]
Step-by-step explanation:
First, plot the two points. We can see the focus is below the vertex. The result will be a vertical parabola. Since the parabola must contain the focus, it will have to open downward.
From this information, we know that the following equation must be used:
[tex](x-h)^2=-4p(y-k)[/tex]
where (h,k) is the vertex and p is the distance from the focus to the vertex.
Next, find p, the distance between the focus and vertex. We can use the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The vertex is (0,0) and the focus is (0, -1/2). Therefore:
[tex]x_1=0\\y_1=0\\x_2=0\\y_2= -1/2[/tex]
[tex]d=\sqrt{(0-0)^2+(0--1/2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(0+1/2)^2}[/tex]
[tex]d=\sqrt{0+(1/2)^2}[/tex]
[tex]d=\sqrt{0+1/4}[/tex]
[tex]d=\sqrt{1/4}[/tex]
[tex]d=1/2[/tex]
Now we know the distance and vertex. We can plug the values into the equation.
d=1/2 and (h,k)= (0,0)
[tex](x-0)^2=-4(1/2)(y-0)[/tex]
[tex](x)^2=-2(y)[/tex]
[tex]x^2=-2y[/tex]
The equation of the parabola is x²= -2y
[/tex]Focus: [tex](0,-\dfrac{1}{2})[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/bgrGPTOi9vAl44ZCMe6evC5L9JnwbXcX.png)
Related Questions
If you want to buy an item in a store that costs $32.50 and is on sale for 30% off, then how much would the item actually cost you after the discount? Round to the nearest cent.
Answers
Answer:
22.80
Step-by-step explanation:
100% - 30% = 70% that you'll be paying
70% = [tex]\frac{70}{100}[/tex] = 0.7
0.7 * 32.50 = 22.75
Round to nearest cent: 22.8
Create a 5th degree trinomial that has a constant term of 3.
Answers
Answer:
[tex]2x^5+3x^2+3[/tex] is a trinomial having with:
three terms degree 5 and The constant term '3'Step-by-step explanation:
Considering the trinomial
[tex]2x^5+3x^2+3[/tex]
Any polynomial with 3 terms is a trinomial, so it is a trinomial.It is clear that '5' is the highest power of the 'x' variable. so, the polynomial has a degree of 5.
'3' is the constant term. The reason is that any term with no variable is called a 'constant' term. So, '3' is the constant term.
Therefore, [tex]2x^5+3x^2+3[/tex] is a trinomial having with:
three terms degree 5 and The constant term '3'molly bought a lunch special that was originally $14 today it is on sale for 20% off what is the sale price of the lunch special
Answers
The sale price is $2.80
14 - 2.80 = 11.20
The sale price is $11.20
A local specialty store sells two brands of yogurt. Brand A is a fruit yogurt that comes in a 12-ounce container for $2.88. Brand B is a fruit yogurt that comes in a 16-ounce container for $4.48. Which one is a better buy: Brand A or Brand B?
Answers
Answer:
0.04
Step-by-step explanation:
Brand A:
so x is equal to 0.24
Brand B:
so x is equal to 0.28
Now the difference of cost would be Brand B - Brand A which would give you 0.04.
What is the minimum value for the function shown in the graph?
(pls help asap thank you :^)
Answers
what is 5 times 10 to the sixth power times 5 times 10 to the seventh power in scientific notation
Answers
Answer:
The Answer for this question in scientific notation is:
2.5e+14
Answer:
5 · [tex]10^{13}[/tex]
Step-by-step explanation:
hope this helps
can someone help me please
Answers
Answer:
6 (x)
Step-by-step explanation:
A newspaper is rolled into a cylindrical shape of approximate diameter 4cm It is wrapped for posting with a strip of paper which goes about 2 1/2 times round the newspaper Use the value 3 for π to find the approximate length of the wrapping paper. And 2. Calculate the total surface area of a solid cone of slant hight 10cm and base diameter 10 cm.Use the value 3.14 for π
Answers
Answer:
30 cm
[tex]863.5\ \text{cm}^2[/tex]
Step-by-step explanation:
d = Diameter of cylinder = 4 cm
n = Number of times the strip of paper is turned = [tex]2\dfrac{1}{2}=2.5[/tex]
Diameter of the cylinder will be approximately equal to the diameter of the paper wound. Length of one turn will be circumference of the paper
Circumference of the paper
[tex]c=\pi d\\\Rightarrow c=3\times 4\\\Rightarrow c=12\ \text{cm}[/tex]
Total length of the paper will be the number of turns multiplied by the length of one turn
[tex]l=nc\\\Rightarrow l=2.5\times 12\\\Rightarrow l=30\ \text{cm}[/tex]
Length of the strip of paper is 30 cm.
2.
l = Slant height = 10 cm
d = Base diameter = 10 cm
r = Radius of base = [tex]r=\dfrac{d}{2}=\dfrac{10}{2}=5\ \text{cm}[/tex]
Total surface area of cone is given by
[tex]S=\pi r^2+\pi rl\\\Rightarrow S=\pi r(r+rl)\\\Rightarrow S=3.14\times 5(5+5\times10)\\\Rightarrow S=863.5\ \text{cm}^2[/tex]
The total surface area of cone is [tex]863.5\ \text{cm}^2[/tex].
3x-2(x+5)=14 then x
Answers
3x -2x -10 = 14
x -10 =14
10. 10. add 10 to both sides
x = 24
:)
Answer:
x = 24
Step-by-step explanation:
3x-2(x-5)=14
remove the parentheses using distributive property
3x-2x-10=14
collect like terms
x-10=14
move constant to the right side and change the sign
x=14+10
calculate ( add the numbers together)
x = 24
Reflections of the coordinate plane homework 3
Answers
Answer:
can we have more info please?
Step-by-step explanation:
Julio says, "If you subtract 13 from my number and multiply the difference by -3, the result is -54 ." What is Julios's number?
Answers
Answer:Julios's number is 31
suppose: Julios's number is x
because Julio says, "If you subtract 13 from my number and multiply the difference by -3, the result is -54 "
=> we have: (x - 13).(-3) = -54
<=> x - 13 = (-54):(-3) = 18
<=> x = 18 + 13 = 31
<=> x = 31
Step-by-step explanation:
Betty bought 3 packages of chocolate cupcakes and 7 packages of vanilla cupcakes. Each package contains 24 cupcakes. Which equation is NOT a way to find c, the number of cupcakes Betty bought in all?
Answers
Answer:
The equation to find the number did cupcakes bought in all =
= 3c + 7c
= c(3 + 7)
The total number Betty bought in all = 240 cupcakes.
Step-by-step explanation:
Let the amount of cupcakes in a package be represented by c
Betty bought 3 packages of chocolate cupcakes and 7 packages of vanilla cupcakes.
The equation to find the number did cupcakes bought in all =
3 × c + 7 × c
= 3c + 7c
= c(3 + 7)
Each package contains 24 cupcakes
The total number = 3(24) + 7(24)
= 240 cupcakes.
Solve the equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.
x = -3 and 1
x = -2
No real roots.
x = 3 and -1
Answers
Answer:
No real roots.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define
-3x² + 2x = 1
Step 2: Rewrite in Standard Form
Subtract 1 on both sides: -3x² + 2x - 1 = 0Step 3: Define
a = -3
b = 2
c = -1
Step 4: Find roots
Substitute in variables: [tex]x=\frac{-2\pm\sqrt{2^2-4(-3)(-1)} }{2(-3)}[/tex]Exponents: [tex]x=\frac{-2\pm\sqrt{4-4(-3)(-1)} }{2(-3)}[/tex]Multiply: [tex]x=\frac{-2\pm\sqrt{4-12} }{-6}[/tex]Subtract: [tex]x=\frac{-2\pm\sqrt{-8} }{-6}[/tex]Here we see that we cannot take the square root of a negative number. We will get no real roots and only imaginary ones.
Find the surface area of the prism
Answers
Answer:
the answer is 29
Step-by-step explanation:
CORRECT ANSWER GETS BRAINLIEST !
Vana lives 6 miles from the library and 18 miles from the museum . To the nearest mile . What is the shortest distance from the museum to the library ?
A.16mi
B.17mi
C.19mi
D.20mi
Answers
Answer:
C
Step-by-step explanation:
I just took the quiz :D
May I have Brainiest???
There are some nickles,dimes and quarters in a large piggy bank.For every 2 nickles there are 3 dimes.For every 2 dimes there are 5 quarters.There are 500 coins total.How many Nickles,Dimes and Quarters are in the piggy bank?
Answers
Answer:
I have no clue
Step-by-step explanation:
Which expression is equivalent to 735 ÷ 100?
7.35 ÷ 1000
735 x 0.01
735 x 0.001
73.5 ÷ 100
Answers
Answer:
735x0.01
Step-by-step explanation:
Which number is rational?
1. –2.1010010001...
2. –0.8974512...
3. 1.2547569...
4. 5.3333333...
PLEASE HELP ITS A UNIT TEST AND TIMED
Answers
Answer:
4.) 5.3333333....
Step-by-step explanation:
Rational numbers are either repeating decimals:
[tex]\frac{1}{3}= 0.333333333....[/tex]
Include terminating decimals:
[tex]\frac{1}{8}= 0.125[/tex]
Are all numbers that can be written as a quotient of integers:
[tex]\frac{a}{b},b\neq 0[/tex]
Options (1), (2), and (3) are neither repeating, terminating, and can't be written as a quotient of integers.
Option (4) has repeating decimals, so this is rational.
:Done
Translate the sentence six less than the product of four and a number is -2 into an equation
Answers
Answer:
4x-6=-2
Step-by-step explanation:
This is the mathematical form of the equation.
2. Which system of inequalities are represented by the graph below:
a) y 2x + 4
y<-x + 4
b) y> 2x + 4
y <-X + 4
c) Y S-2x + 4
y>X-2
d) y 2x + 4
YS-X+4
tem of equations have?
Answers
Answer:
12
Step-by-step explanation:
Use the slope-intercept form y=mx+b to find the slope m and y-intercept b
.
Slope: 12
y-intercept: (0,−2)
Can someone please explain how to find the answer? My old teacher didn’t do it this way and I’m lost :/
Answers
Answer:
the triangle means "change in". so triangle x means the change in the x values and triangle y means change in y values so yeah mental calculate the difference
find x (11x-1) (20x-3) 151
Answers
Answer:
x=5 I think
Step-by-step explanation:
just search it up online
Tracy spends $97 on her cell phone bill this month. Her bill is usually around the same amount each month. If she wants to include an estimate of her cell phone bill in her monthly budget, what amount should she use? Round to the nearest ten.
Answers
Answer:
$100
Step-by-step explanation:
97 is rounded to 100 because the last digit is more that 5.
I hope this helped, please mark Brainliest, thank you!
0.3x-2.4=1.25x
How to solve
Answers
Answer:
hi
Step-by-step explanation:
0
.
3
−
2
.
4
=
1
.
2
5
0.3x-2.4=1.25x
0.3x−2.4=1.25x
3
1
0
−
2
.
4
=
1
.
2
5
Answer:
x = -2.52631578
Step-by-step explanation:
Combine multiplied terms into a single fraction.
0.3x - 2.4 = 12.5x
3x/10 - 2.4= 1.25x
Again, combine multiplied terms into a single fraction.
3x/10 - 2.4= 1.25x
3x/10 - 2.4 = 5x/4
Add 2.4 to both sides of the equation
3x/10 - 2.4 = 5x/4
3x/10 - 2.4 + 2.4 = 5x/4 + 2.4
Simplify (Add the numbers)
3x/10 = 5x/4 + 2.4
Multiply all terms by the same value to eliminate fraction denominators.
3x/10 = 5x/4 + 2.4
2 x 2 x 5 x 3x/10 = 2 x 2 x 5(5x/4 +2.4)
Therefor, x = 2.52631578
Hope this helps, have a great day! :)
Joseph has 1/2 of a sub left after lunch. He eats 1/4 of this amount for snack. what fraction of a whole sub did Joseph eat for snack
Answers
Answer:
Step-by-step explanation:
I believe the answer would be 1/4 of the sub. Because they asked about the whole sub. And it says he ate 1/4 of the amount of that half of the sub for snack. So out of the whole sandwich it would be 1/4!
If it’s not the answer your looking for you can take it off...
But...
Hope it helps
300% of 82 is what number?
Answers
Answer:246
Step-by-step explanation:
A circle has a diameter of 26 mm. What Is Its circumference?
Use 3.14 for 1, and do not round your answer. Be sure to Include the correct unit in your answer
Answers
The formula for circumference is 2 x pi x radius
In order to find the radius you need to divide 26 by 2
26 divide by 2 is equal to 13
2 x 3.14 x 13= 81.681 or 26pi
Robert says he needs 250 plastic sleevs for his basball card collection.He has 3084 baseball cards.Each sleev holds 12 cards do you agree whith robert
Answers
Answer:
No
Step-by-step explanation:
Given that:
Plastic sleeves needed = 250
Number of baseball cards = 3084
Sleeves held per card = 12
To determine the number of sleeves needed ;
Number of baseball cards / number of sleeves per card
= 3084 / 12
= 257
No, I do not agree with Roberts, from the calculation above, the number of plastic sleeves needed is 257
find the value of x that makes m|n
Answers
Answer:
x = 60°
Step-by-step explanation:
Two parallel lines will have the same angle if another line intersects them. That means 2x+15° = 135°.
2x = 120°
x = 60°
Answer:
opposite number of -18
OMGGG CAN YALL ANSWER THIS !
In a newspaper, it was reported that the number of yearly robberies in Springfield in 2012 was 90, and then went down by 50% in 2013. How many robberies were there in Springfield in 2013?
Answers
Answer:
m
Step-by-step explanation:
m
Answer:
There were 140 robberies in Springfield in 2012.
Step-by-step explanation:
Let's marked (named) robberies in 2012 with x, which is worth 100%
196 robberies in 2013 worth 100% + 40% = 140%
Now we will make proportion
x : 196 = 100 : 140
When we multiply external and internal members we get
140 x = 196 · 100 => 140 x = 19600 => x = 19600/140 = 140
x = 140 robberies in 2012