The function f(t) = t2 + 4t - 14 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your
work.

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on
the graph. How do you know?

Part C: Determine the axis of symmetry for f(t).

Answers

Answer 1

Answer:

a: [tex]f(t)=(t+2)^2-18[/tex]

b: vertex: (-2, -18)

   minimum

c: x = -2

Step-by-step explanation:

Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.

Part A ===============

Start with the given function in this form:

[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]

We need an additional number, d, and we'll calculate it like this:

[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]

d needs to be added and subtracted at the same time. That way we do not change the value of the expression:

[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]

And you can separate them like this to make it easier to read:

[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]

Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial.  The factored form is just:

[tex](x+e)^2[/tex]

where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.

[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]

Put that all together and you get the answer:

[tex]f(t)=(t+2)^2-18[/tex]

Part B ===============

Vertex form is this:

[tex]f(x)=a(x-h)^2+k[/tex]

where (h, k) is the vertex and a is the scale factor.

In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.

The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.

Part C ==============

The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.

The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.

Sorry if that got too long and hard to follow, I can clarify any part of it if needed.


Related Questions

If a shirt cost $60 is on sale for 50% off and you have another offer that gives you an additional 20% off the sale price does that mean you get a total of 70% off show your work to justify your answer

Answers

Answer:

No

Step-by-step explanation:

50 % off $60 =$30

20% off $30 =$6

But 70% =42

Therefore it's not the same as 70%

$200 is shared between Bill and Ann. Ann’s share is $50 more than Bill’s share. Calculate the size of each of their shares.

Answers

First subtract the difference between the two:

200 - 50 = 150

Now divide that by 2:

150/2 = 75

Bills share is $75

Now add the $50 to 75 to get Ann's share:

75 + 50 = $125

Ann's share is $125

Bill's share is $75

Is the following a reflection,
rotation or translation?

Answers

This is a translation

In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
On any given Sunday, are you more likely to only be in church, more likely to only be watching football, doing both, or doing neither?

(a) To only be in church [269 respondents selected this answer]

(b) To only be watching football [175 respondents selected this answer]

(c) Doing both [217 respondents selected this answer]

(d) Doing neither [372 respondents selected this answer]
Create a 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday.

Answers

Using the z-distribution, it is found that the 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday is (23.36%, 28.72%).

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].

269 out of 1033 respondents said they were likely to only be in church, hence:

[tex]n = 1033, \pi = \frac{269}{1033} = 0.2604[/tex]

95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2604 - 1.96\sqrt{\frac{0.2604(0.7396)}{1033}} = 0.2336[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2604 + 1.96\sqrt{\frac{0.2604(0.7396)}{1033}} = 0.2872[/tex]

As a percentage:

0.2336 x 100% = 23.36%

0.2872 x 100% = 28.72%

The 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday is (23.36%, 28.72%).

A similar problem is given at https://brainly.com/question/25743435

I need to know how to subtract fractions 4 2/3 - 3/4

Answers

Answer: The answer would be 3.91666666667

[tex]\huge\textsf{Hey there!}[/tex]


[tex]\mathsf{4 \dfrac{2}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{4\times3+2}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{12 + 2}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{14}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{56}{11} - \dfrac{9}{12}}[/tex]

[tex]\mathsf{= \dfrac{14\times4}{12 - 0}}[/tex]

[tex]\mathsf{= \dfrac{56 - 9}{12}}[/tex]

[tex]\mathsf{= \dfrac{47}{12}}[/tex]

[tex]\mathsf{= 3 \dfrac{11}{12}}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: }\huge\boxed{\\\mathsf{\dfrac{47}{12} \ or\ 3 \dfrac{11}{12}}}\huge\checkmark[/tex]



[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]



~[tex]\frak{Amphitrite1040:)}[/tex]

tal) In a survey of 185 college students, they were asked whether they have dogs, cats,

or birds as pets:

90 have dogs,

68 have cats,

8 have birds only,

15 have both cats and dogs only,

20 have both birds and dogs,

12 have both cats and birds, and

7 students have all three animals as pets


a). Draw a Venn diagram to represent the given information.

b). How many students have cats only?

c). What proportion of the students have exactly one type of animal as pets?

Answers

9514 1404 393

Answer:

  a) see attached

  b) 41

  c) 56.2%

Step-by-step explanation:

a) We have drawn three circles, labeled D, C, B representing students who have dogs, cats, and birds, respectively. Based on the given information we can fill numbers in for all three animals (7), cats and dogs only (15), and birds only (8).

Then we can fill in cats and birds only by subtracting the number with all three. That will be 12 -7 = 5. Birds and dogs only is similarly filled by subtracting all three to get 20 -7 = 13 birds and dogs only.

Dogs only is found by subtracting the numbers in multiple categories from the total number of dogs: 90 -13 -7 -15 = 55. Cats only is found the same way: 68 -5 -7 -15 = 41.

The completed diagram is shown in the attachment. (We haven't figured the quantity for "none.")

__

b) 41 students have cats only

__

c) The total number with dogs only, cats only, or birds only is ...

  55 +41 +8 = 104

Of the 185 total students, that is 104/185 ≈ 56.2%.

56.2% of students have exactly one type of animal as a pet.

In a recent tennis​ tournament, women playing singles matches used challenges on 133 calls made by the line judges. Among those​ challenges, 31 were found to be successful with the call overturned. a. Construct a 90​% confidence interval for the percentage of successful challenges. b. Compare the results from part​ (a) to this ​90% confidence interval for the percentage of successful challenges made by the men playing singles​ matches: ​20.9%

Answers

Using the z-distribution, it is found that the 90​% confidence interval for the percentage of successful challenges is (17.28, 29.34).

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].

31 out of 133 challenges were successful, hence:

[tex]n = 133, \pi = \frac{31}{133} = 0.2331[/tex]

90% confidence level, hence [tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 - 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.1728[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 + 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.2934[/tex]

As percentages:

0.1728 x 100% = 17.28%

0.2934 x 100% = 29.34%

The 90​% confidence interval for the percentage of successful challenges is (17.28, 29.34).

A similar problem is given at https://brainly.com/question/16807970

Look at picture for question.

Answers

Answer:

A) - 3/7

B) -1/5

C) - 0.4

Step-by-step explanation:

HOPE IT CAN HELP YOU LOVELOTS

9) You want to buy a backpack which costs $34.82. Now it is on sale of 30% off. What is the
discount amount? What is the final cost with the discount?

Answers

Answer:

10.446

Step-by-step explanation:

Travel agents collected data from recent travelers about their modes of transportation for their vacations, They found that 37% traveled by airplane, 8% traveled by train, and 7% traveled by airplane and train. Let A be the event that the mode of travel was airplane and let T be the event that the mode of travel was train.​

Answers

Using Venn probabilities, it is found that the probability is [tex]P(A \cap T^{c}) = 0.3[/tex]

In this problem, the events are:

Event A: Traveled by airplane.Event T: Traveled by train.Event [tex]T^{c}[/tex]: Did not travel by train.

The desired probability is:

[tex]P(A \cap T^{c}) = P(A) + P(T^{c}) - P(A \cup T^{c})[/tex]

The probabilities are:

37% traveled by airplane, hence [tex]P(A) = 0.37[/tex]8% traveled by train, hence [tex]P(T^c) = 1 - 0.08 = 0.92[/tex]37% traveled by airplane, 62%(100 - [37 + 8 - 7]) did not travel, hence [tex]P(A \cup T^c) = 0.37 + 0.62 = 0.99[/tex]

Then:

[tex]P(A \cap T^{c}) = P(A) + P(T^{c}) - P(A \cup T^{c})[/tex]

[tex]P(A \cap T^{c}) = 0.37 + 0.92 - 0.99[/tex]

[tex]P(A \cap T^{c}) = 0.3[/tex]

A similar problem is given at https://brainly.com/question/24707032

Answer:

B: .30

Step-by-step explanation:

edg 2021

A hummingbird lives in a nest that is 12 meters high in a tree. The hummingbird flies 15
meters to get from its nest to a flower on the ground. How far is the flower from the base of
the tree?

Answers

Answer:

The flower is 9 meters from the base of the tree.

Step-by-step explanation:

Use the Pythagorean theorem to solve. We are given the length of one leg and the length of the hypotenuse of a right triangle.

[tex]a^{2} +b^{2} =c^{2}[/tex]

where a and b are the legs, and c is the hypotenuse.

Plug in the given values and solve:

[tex]x^{2} +12^{2} =15^{2} \\x^{2} +144=255\\x^{2} =81\\x=9[/tex]

The flower is 9 meters from the base of the tree.

need help asap PLS HURRY

Answers

Use a graphing calculator to find which points match up to the functions. (But it’s the 4th answer!)

logx=(logx)^2
find the value of x without using calculator


Answers

Answer:

x = 1

Step-by-step explanation:

log(1) = 0

log(1) = [tex]log(1)^{2}[/tex]

0 = [tex]0^{2}[/tex]

0 = 0

Anne bought an aquarium priced at $44.96. Shipping and handling cost an additional 25%of the price. What was the total cost of the aquarium, including shipping and handling?

Answers

25% of 44.96 is found by dividing 44.96 by 4. 11.24 + 44.96 is 56.2

The speed of an object is the ratio of its distance traveled to time. If the speed of a bicycle is 4.5 meters per second, what is the distance traveled in 9 seconds?

Answers

Answer:

40.5 meters

Step-by-step explanation:

4.5m/s • 9s = 40.5m

Identify each equation as direct variation, an inverse variation or neither. 6. m=2n 7. y = 6/w 8. st = 18 9. k= 42h 10. p = 3-4​

Answers

Answer:

tnx to your points..

god bless you ..

maybe they help for youuu..

The mean number of accidents per month at a certain intersection is 1. a) What is the probability that in any given year at least 3 accidents (including 3 accidents) will occur at this intersection? [10 points] b) What’s the mean and variance for the number of accident for a given year? [10 points]

Answers

Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

(1) mean value = 6

use excel function POISSON(x,mean,cumulative)

set x = 4, mean =6 and cumulative = TRUE

P(X>4) =1 -POISSON(4,6,TRUE) = 0.7149

(2) mean value = 6

use excel function POISSON(x,mean,cumulative)

set x = 1, mean =6 and cumulative = TRUE

P(X \le 1) =POISSON(1,6,TRUE) = 0.0174

can some one help me solve this​

Answers

Answer:

time = 0.4, height = 24.8m

Step-by-step explanation:

We need to find the coordinates of the vertex of the parabola.

[tex]f(x)=ax^2+bx+c\\\\v(p,\ q)-\text{vertex}\\\\p=\dfrac{-b}{2a};\ q=f(p)[/tex]

We have

[tex]h(t)=24+4t-5t^2=-5t^2+4t+24\\\\a=-5,\ b=4;\ c=24\\\\p=\dfrac{-4}{2(-5)}=\dfrac{-2}{-5}=\dfrac{2}{5}=0.4\\\\q=h(0.4)=-5(0.4)^2+4(0.4)+24=-5(0.16)+1.6+24\\\\=-0.8+25.6=24.8[/tex]

Dylan had 300 5p coins in a box last month. He now has 360 5p coins. Find the percentage increase.

Answers

300 + 60 = 360360 ÷ 5 = 72

Therefore the percentage increase is 72

72

$1689 invested for 4 years at 3% compounded annually ?

Answers

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

The amount of money gained after an investment is compounded is given by:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Where P is principal, A is the final amount, r is the rate, n is the number of times compounded per period and t is the time

Given that P = $1689, t = 4, r = 3% = 0.03, n = 1, hence:

[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=1689(1+\frac{0.03}{1} )^{4*1}\\\\A=\$1901[/tex]

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

Find out more at: https://brainly.com/question/14295570

What is 3/4+1 2/3+1/2=

Answers

35/12 is the correct answer

Answer:

Exact Form:

35/12

Decimal Form:

2.916- (6 goes on)

Mixed Number Form:

2 11/12

A circular garden has a diameter of 10 feet approximately how much edging trim is needed to surround the garden by placing the trim all along the gardens circumference

Answers

Answer: 31.4 feet

Step-by-step explanation:

For this, you basically need to calculate the perimeter of the circle. You do this using this formula:

diameter of the circle times Pie = the circumference of the circle

Since The number of Pie is infinite use the rounded version of pie to 2 decimal points which is 3.14(This is why the question asks for an approximate)

(Diameter = 10 Pie = 3.14 therefore circumference = 31.4)

10 times 3.14 = 31.4 feet

The amount of edging trim needed to surround the garden by placing the trim all along the gardens circumference is 31.4 ft.

The garden is circular in shape. Thereforem the trim that is needed to surround the garden is the circumfernce of the graden.

Circumference of a circle

The circumference of a circle is the perimeter of the circle. Therefore,

circumference = 2πr

where

r = radius

Therefore, the amount of edging trim needed to surround the garden by placing the trim all along the gardens circumference is as follows:

circumference = 2 × 3.14 × 5

circumference = 10 × 3.14

circumference = 31.4 ft

learn more on circumference here: https://brainly.com/question/25730499


Find the length of a diagonal of a 6 inch square.


Answers

Answer:

Step-by-step explanation:

If square is split into two from diagonal then it forms two right angled triangles which are congruent.

Therefore we can use Pythagoras theorem as we know side

d^2=6^2+6^2

d=√72

d=6√2

d=8.485 inches

Method 2:

Using formula

d=s√2

d=6√2

d=8.485 inches

You can find length of diagonal of any square if you know the length of side using formula.

d=s√2

Where s is length of side

Where is the point (0, -2) located on the coordinate plane?
A. On the y-axis
B. On the x-axis
O C. In quadrant III
D. In quadrant IV

Answers

Answer:

A

Step-by-step explanation:

The x- coordinate of any point on the y- axis is zero, that is (0, c ) , then

(0, - 2 ) is located on the y- axis

Sara left a bin outside in her garden to collect rainwater. She notices that one over eight gallon of water fills two over three of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.

Answers

Answer:

3/16

Step-by-step explanation:

In order to get the amount of water to fill a bin, we just divide the amount of water by the fraction of the bin it fills. This makes the unit of the resulting answer as gallons/bin or gallons per bin.

Please help! Will give 50 points!!

Answers

Answer:

- 5 | - 1 | 3 | 7

Step-by-step explanation:

Given function:

y = 2x + 3

Complete table by finding y values:

x = - 4  ⇒ y = 2*(-4) + 3 = - 8 + 3 = - 5x = - 2 ⇒ y = 2*(-2) + 3 = - 4 + 3 = - 1x = 0  ⇒ y = 2*0 + 3 = 0 + 3 = 3x = 2  ⇒ y = 2*2 + 3 = 4 + 3 = 7

Help please on part b

Answers

Answer:

-0.045

Step-by-step explanation:

you first take the derivate of A(t)

A'(t)=1.4e^-0.05t X (-0.05)

A'(t)=-0.07e^-0.05t

so when t=0

amount remaining is -0.07e^-0.05(0) ---- e^0 = 1

so its -0.07

when t=9

do the same thing,

-0.07e^-0.05(9) ---use calculator

-0.045

What is the slope of the line that passes through the points (6, -10) and (3, -13)?
Write your answer in simplest form.

Answers

[tex](x_1, y_1) = (6,-10),~~ (x_2, y_2) = (3,-13)\\\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-13 +10}{3 -6} =\dfrac{-3}{-3} =1[/tex]

Hello, can you help me?, thank you​

Answers

Answer:105216

Step-by-step explanation:17,536*6=105216

Answer:

105,216

Step-by-step explanation:

17,536*6

Can someone help me on theses?

Answers

For question 3 it will be. -4,11,-3,3,0,-22
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