What is the focus of the parabola? y=−1/4x^2 −2x − 2

Answers

Answer 1

Answer:

Step-by-step explanation:

This is a doozy. You have to know A LOT about parabolas to get to this answer. First and foremost, we will have to complete the square on the x terms and get everything else on the other side of the equals sign with the intention of putting this into standard form which looks like this:

[tex]-4p(y-k)=(x-h)^2[/tex]

The negative is because the parabola is upside down. We begin breaking it down by multiplying everything by -4 to get:

[tex]-4y=x^2+8x+8[/tex] and subtract that 8 from both sides to get:

[tex]-4y-8=x^2+8x[/tex]. Now we'll complete the square on the x terms by taking half the linear term, squaring it, and then adding it to both sides. Our linear term (the number with the x stuck to it) is 8. Half of 8 is 4 ad 4 squared is 16. So we add 16 to both sides to get:

[tex]-4y-8+16=(x^2+8x+16)[/tex]

The right side will simplify into a perfect square binomial and the left side we will just combine like terms to get:

[tex]-4y+8=(x+4)^2[/tex]

We're getting close. Now we need to just factor out the -4 on the left to get:

[tex]-4(y-2)=(x+4)^2[/tex]

If the standard form is -4p blah blah blah, then p has to be 1. That means that the focus is 1 unit below the vertex. The vertex is (-4, 2). p is the distance between the vertex and the focus. The focus is always on the axis of symmetry. We know that the parabola opens upside down because of the negative sign, and the parabola always wraps itself around the focus. That's why the focus is p units below the vertex. That means that the focus is located at (-4, 1).

Told you it was difficult. I noticed no one helped you with this one and it's been up here for 5 days...


Related Questions

I need help with math homework #2 algebra

Answers

Answer:

A. (0, -2) and (4, 1)

B. Slope (m) = ¾

C. y - 1 = ¾(x - 4)

D. y = ¾x - 2

E. -¾x + y = -2

Step-by-step explanation:

A. Two points on the line from the graph are: (0, -2) and (4, 1)

B. The slope can be calculated using two points, (0, -2) and (4, 1):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 -(-2)}{4 - 0} = \frac{3}{4} [/tex]

Slope (m) = ¾

C. Equation in point-slope form is represented as y - b = m(x - a). Where,

(a, b) = any point on the graph.

m = slope.

Substitute (a, b) = (4, 1), and m = ¾ into the point-slope equation, y - b = m(x - a).

Thus:

y - 1 = ¾(x - 4)

D. Equation in slope-intercept form, can be written as y = mx + b.

Thus, using the equation in (C), rewrite to get the equation in slope-intercept form.

y - 1 = ¾(x - 4)

4(y - 1) = 3(x - 4)

4y - 4 = 3x - 12

4y = 3x - 12 + 4

4y = 3x - 8

y = ¾x - 8/4

y = ¾x - 2

E. Convert the equation in (D) to standard form:

y = ¾x - 2

-¾x + y = -2

Please help if you can
Tia dilated the rectangle below by a scale factor of 7/2. What is ther perimeter of the new rectangle?
A
64 inches

B
220 inches

C
2695 inches

D
224 inches

Answers

Answer:

Option D

Step-by-step explanation:

Formula to be used,

Scale factor = [tex]\frac{\text{Dimension of the image rectangle}}{\text{Dimension of the original}}[/tex]

By this formula,

[tex]\frac{7}{2}=\frac{\text{Length of the dilated rectangle}}{\text{Length of the original rectangle}}[/tex]

[tex]\frac{7}{2}=\frac{L}{22}[/tex]

L = [tex]\frac{7\times 22}{2}[/tex]

  = 77 inches

Similarly, width of the the dilated rectangle = [tex]\frac{7}{2}\times 10[/tex]

                                                                        = 35 inches

Perimeter of the new rectangle = 2(Length + width)

                                                    = 2(77 + 35)

                                                    = 224 inches

Option (D) will be the correct option.

27.1018494699 round to nearest hundred-thousandth

Answers

Answer:

27.101

Step-by-step explanation:

Ethan has saved $180 to buy a bicycle which costs $540. He wants to find how much more he needs to save to buy the bicycle
Which equation when solved would show Ethan the amount of money he needs to save?

Answers

Answer:

X = 360

Step-by-step explanation:

180 + x = 540

-180 = -180

Answer:

540-180=360

Step-by-step explanation:

Why? Because he has 180, he need 540. There is 360 in between, which is the money he needs.

Hope this is the right equation.

Identify the vertex of
y = 2x2 − 4x − 2

Answers

vertex at

(

1

,

4

)

Explanation:

Given:

y

=

2

x

2

+

4

x

2

Convert the given form into "vertex form"

y

=

m

(

x

a

)

2

+

b

with vertex at

(

a

,

b

)

XXX

y

=

2

(

x

2

+

2

x

)

2

complete the square

XXX

y

=

2

(

x

2

+

2

x

+

1

)

2

2

XXX

y

=

2

(

x

+

1

)

2

4

XXX

y

=

2

(

x

(

1

)

)

2

+

(

4

)

which is the vertex form with vertex at

(

1

,

4

)

graph{2x^2+4x-2 [-5.455, 7.034, -5.54, 0

The answer is (1,-4)

3 inches
1.5 inches
1.5 inches

Answers

Answer:

6 inches

Step-by-step explanation:

4 × 22 + 16 ÷ 4 - (4.9 + 5.5)

Answers

Answer:

81.6

Step-by-step explanation:

4 × 22 + 16 ÷ 4 - (4.9 + 5.5)

88 + 4 - (10.4)

81.6

Pleaseee Helppppp
Find the minimum value of the function f(x) = x2 + 12x + 31.5 to the
nearest hundredth.

Answers

Answer:

The answer is pie

Step-by-step explanation:

I know best

Answer:

x = -6.00 (rounded to nearest hundredth)

Step-by-step explanation:

for a quadratic equation, [tex]h(x)=ax^2+bx+c[/tex]  we have [tex]f(x)=x^2+12x+31.5[/tex] a = 1 b = 12 to find minimum use equation [tex]x=\frac{-b}{2a}[/tex] [tex]x=\frac{-b}{2a}\\x=\frac{-(12)}{2(1)}\\x=\frac{-12}{2}=-6[/tex]

how to give points
nsdfjfjrs d,nvcnjsd

Answers

Answer: answer questions

Step-by-step explanation:

Answer:

tyyyy hope you have a good holiday !!!!!!!

<3333

PLEASEEEEE IM DESPITE Xd-
Anyone
Will mark branliest

Answers

Answer:

B 8.42 seconds

Step-by-step explanation:

421 in 50 seconds

421//50

8.42 seconds

Hope this helps!

Most likely B, because if you divide 421 and 50, you will get the inches per sec.


If two lines are perpendicular, their slopes are negative reciprocals.
A. True
B.False

Answers

A. If the slopes of two lines are negative then the reciprocals, of the lines are perpendicular.
THE ANSWER IS TRUE I’M 100%

You are hiking in the woods at a rate of 3 mph. The function y=3x describes how many miles y you walk in x hours. create an input table with 3 domain values

Answers

Answer:

x ---- y

1 ---- 3

4 ---- 12

6 ---- 18

Step-by-step explanation:

Given

[tex]y = 3x[/tex]

Required

Create a table that represents this scenario

Because x represents time, x can not be negative. So, the domain of x is:

[tex]x \geq 0[/tex]

Assume [tex]x = 1[/tex]

[tex]y = 3 * 1 = 3[/tex]

Assume x = 4

[tex]y=3*4 = 12[/tex]

Assume x = 6

[tex]y=3*6 = 18[/tex]

Hence, the table is:

x ---- y

1 ---- 3

4 ---- 12

6 ---- 18

math question!
please answer for 10+ points

Answers

Answer:

5 to the fourth power is 625

625 / 25 is 25

so now you have 25 = 5 to the second power

and five to the second power is 25

Step-by-step explanation:

So the answer should be the third one.

the answer is 15 I had the same question

It says to classify what does this mean I be dumb

Answers


for 10 x = 28.

8x-44=180
+44. +44

8x=224

224/8=28

Solve 4x+34 help please

Answers

9514 1404 393

Answer:

  78

Step-by-step explanation:

The base (JL) is twice the length of the midline (MN), so you have ...

  4x +34 = 2(5x -16)

  4x +34 = 10x -32 . . . eliminate parentheses

  66 = 6x . . . . . . . . add 32-4x

  11 = x

Then the length of JL is ...

  4(11) +34 = 78

(a) 12 is 15% of what?

Answers

80


hope this helps mate

Jina's dance recital started at 4:46 PM. It ended at 6:13 PM. How long did the recital last?

Answers

Answer:

Jina's recital lasted 2 hours and 7 minutes

Hope that helped

Step-by-step explanation:

Answer:

2 hour and 7 minutes is the answer

someone help me with this

Answers

Answer:

-30 is the right one if u need help tell me ;)-

Step-by-step explanation:

:)

(m²+mn+n²)(m²-mn+n²)​

Answers

To be real I don’t know I don’t understand math with all those letters

Answer:

[tex]m^{4\\}[/tex]+[tex]m^{2}[/tex][tex]n^{2}[/tex]+[tex]n^{4}[/tex]

Step-by-step explanation:

If you're distributing each value, I would recommend you to use the lattice method so that you can work on it faster.  Make sure to add the exponents instead of multiplying to have an accurate answer.  Once your done then cross out the ones that would subtract to 0 which would leave you with [tex]m^{4\\}[/tex]+[tex]m^{2}[/tex][tex]n^{2}[/tex]+[tex]n^{4}[/tex] as your final answer if you did it properly.

Help me fast pleaseeeee

Answers

Answer:

y=-2x-2

Step-by-step explanation:

Find slope and y intercept

3n+14=-4 =?
Please do this this right (my grade depends on it)

Answers

Answer:

Step-by-step explanation:

-6

subtract 14 from both sides
3n = -18
divide both sides by 3
n = -6

The results of a survey of 150 students about whether they
own an electronic tablet or a laptop are shown in the two-way
frequency table.

Answers

Answer:

its either quantitive data ( numerical measurements) or categorical data (cannot be expressed using numbers)

Two way frequency table: Pairs categorical values to list frequencies  

Step-by-step explanation:

For example: One hundred students were surveyed about which beverage they chose at lunch. Some of the results are shown in the two-way frrequency table below.

Lunch Bevarage

genders               Juice.           Milk.         Water.     Total

Girl :                     10                  13              17            40

Boy:                     15                  24             21            60

Total:                   25                 37             38      =    100

A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. Answer parts a and b.
a. To what percent of its capacity is the large container filed?
The container is filled to % of the maximum capacity.

Answers

Answer:

The container is filled to 87.5% of the maximum capacity.

Step-by-step explanation:

Given

Maximum capacity of container = m = 64 ounces

Filled capacity=> as it is 8 less than maximum capacity = 64-8 = 56 ounces

The container is 56 ounces full.

To find the percentage:

[tex]percentage = \frac{56}{64}*100\\= 0.875*100\\=87.5\%[/tex]

Hence,

The container is filled to 87.5% of the maximum capacity.

Holly is making fruit salad. She bought 3 pounds and 3 ounces of fruit. How many ounces of fruit did she buy? *Needed ASAP​

Answers

Answer:

Step-by-step explanation:

do 3 x 16 = 48 + 3 is 51

-1/4 ÷ -3/8
Please Hurry

Answers

Answer:

2 /3 (decimal form ≅ 0.6666667 )

Step-by-step explanation:

Unary minus: -1 /4

= -1 /4

Unary minus: -3 /8

= -3 /8

Divide: the result of step No. 1 : the result of step No. 2 = -1 /4 : (-3 /8 ) =

-1 /4  x -8 /3  = -1 (-8)  divided by 4(3)  = 8 /12  = 4(2 ) divided by 4(3)  = 2 /3

Help!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

D is the correct answer

Step-by-step explanation:

hope it helps

have a great day

:)

can any one help me with this please ?this is worth 82 points

Answers

Answer:

1. YZX

2. XYZ

3. ZXY

4. EDF

5. MLN

6. FED

7. DFE

8. MNL

9. LMN

1 was flipped (reflected).

2 was slid (translated).

3 was slid (translated).

4 was rotated 180 degrees clockwise.

5 was flipped and rotated.

6 was flipped and rotated.

7, 8, 9 were translated.

Kensington was selling Girl Scout cookies and a customer offered her a deal. The customer would place three $1 bills, one $5 bill and one $10 bill in a bag. Kensington would reach into the bag and take one bill from the bag and get paid that instead of the $5 it would cost for one box of Girl Scout cookies. Should she take the deal? Or should she insist on getting the regular cost of $5?

Answers

Answer:

no she should take the deal

Step-by-step explanation:

there are 5 bills in that bag and only 1 of them has a chance of being over the regular price where as 3 have a chance of being under the regurla price the odds a not in the girl scouts favor as she has a 60%chance of not getting a $1 and only a 20% chance of getting the $10.

Solve the system of equation by elimination.

x+2y= -7
-x-2y=8

A. (8,7)
B. No solution
C. (-7,8)
D. (-8,7)

If you can, please explain step by step:)

Answers

Answer: D

Step-by-step explanation:

D. (-8,7) just do it

The population of a city is estimated to decline according to the model P(t)=197000e^-0.014t, where t is the number of years present. What does the model predict the population will be in 13 years?

Answers

N nxhdhshsjshfjfjrjr
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