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3 years ago

F(X)=2(X-1)^2-4 in standard form

Mathematics

1 answer:

trapecia [35]3 years ago

3 0

Answer:

$f(x)=2x^2-4x-2$

Step-by-step explanation:

Standard form of a quadratic equation: $y=ax^2+bx+c$

$\begin{aligned}f(x) & =2(x-1)^2-4\\& =2(x^2-2x+1)-4\\& = 2x^2-4x+2-4\\& = 2x^2-4x-2 \end{aligned}$

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Select all of the statements that are true for the given parabola.

svet-max [94.6K]

Answer:

A and B

Step-by-step explanation:

The minimum occurs at the turning point ( vertex )

The coordinates of the vertex are (1, - 2 ) → A

The x- intercepts are the points where the graph crosses the x- axis

This occurs at (3, 0 ) and (- 1, 0 ) → B

The axis of symmetry is a vertical line passing through the vertex

Equation of axis of symmetry is x = 1 , not y = - 2

(1, - 2 ) is a minimum not a maximum , see above

5 0

4 years ago

Smith engineering is in the process of reviewing the salaries of their surveyors. During this review the company found that expe

crimeas [40]

Answer:

1 hour and 42.85 minutes.

Step-by-step explanation:

It is found from the process of reviewing that experience survey a roadbed in 3 hours.

Hence, in 1 hour the experience survey $\frac{1}{3}$ of the roadbed.

Again, it is found that the apprentice survey needs 4 hours to survey the same stretch of road.

So, in 1 hour the apprentice survey does $\frac{1}{4}$ of the roadbed survey.

If they work together then in 1 hour, the survey work will be done by ( $\frac{1}{3} +\frac{1}{4}$ )= $\frac{7}{12}$ parts.

Therefore, the total survey they will complete working together in $\frac{12}{7}$ hours i.e. 1 hour and 42.85 minutes. (Answer)

3 0

3 years ago

Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an

Law Incorporation [45]

We know that John is hosting an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. . He estimates that for every $2 increases in the fee, the average number of students reduces by 1.

Therefore, we can conclude that his revenue is $14 * 12$ or $168$ bucks.

The session price goes up in a pattern of 2.

For example, from 12 the session price goes to 14, 16, 18 and so on.

As each jumps goes by 2, the amount of students drop by 1.

(i.e from 14 students the number decreases to 13, to 12 and so on.)

As we can see the revenue begins at 168 and continues upward until it reaches 200 dollars and then starts to descend.

This indicates that the U-turn or vertex of the revenue function is approximately 4200, where h represents 4, and k is 200.

To solve we can use Parabola.

⇒ Parabola: any point is at an equivalent separation from:

a settled point (the concentration ), and

a settled straight line (the directrix )

____________________________________________________

$f (x) = a(x - h)^2 + k$ , where (h, k) is the vertex of the parabola.

⇒ $\left \{ {{y=192} \atop {x=2}} \right.$

⇒ $192 = a(2-4)^2+200$

⇒ $-8=a(-2)^2$

⇒ $-8=a*2^2$

⇒ $-8=a*4$

⇒ $-8=4a$

⇒ $-\frac{8}{4} = \alpha$

⇒ $\alpha = -2$

Now lets do the final step: Simplifying

$y-2(x-4)^2+200$ 

$y=-2(x^2-8x+16)+200$

$y=-2x^2+16x-32+200$

$c(x) = -2x^2+16x+168$

3 0

4 years ago

The number of soft pretzels processed by a machine in a bakery varies directly to the number of minutes that the machine runs. T

kolezko [41]

Answer:

the answer is c)

Step-by-step explanation:

the reason is 5*6 would be 30 and if you were to add 3 more zero's, it would be 3000 and 1/10 of 600 is 60 so 60*2 is 120 which is where you het the 120 so you add it up and it's 3,120

7 0

3 years ago

Leanne runs a lap in 12 minutes. Kory runs a lap in 9 minutes. If they

klemol [59]

Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .

Step-by-step explanation:

Here we have , Leanne runs a lap in 12 minutes. Kory runs a lap in 9 minutes. We need to find out that If they both start running at 10 am, at what time will they both cross the start together again . Let's find out:

Kory runs a lap in 9 minutes and , Leanne in 12 minutes , in order to find at what time will they both cross the start together again we will find LCM of 9 & 12 :

⇒ $\frac{9(4)}{12(4)}$

⇒ $\frac{36}{36}$

So ,LCM of 9 & 12 is 36 .That means Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .

In clear way , Kory will run race as :

1st lap = 9 minutes

2nd lap = 18 minutes

3rd lap = 27 minutes

4th lap = 36 minutes , i.e. at 10:36 am he'll complete his 4th lap

For , Leanne

1st lap = 12 minutes

2nd lap = 24 minutes

3rd lap = 36 minutes i.e. at 10:36 am he'll complete his 3rd lap .

This means Kory & Leanne will meet at 10:36 am completing there 4th and 3rd lap respectively .

6 0

4 years ago