4x^2+8x-12 in vertex form

Answers

Answer 1
The answer in vertex form is y=4(x+1)^2 -16
Answer 2

Answer:

y = 4 (x + 1)² - 16

Step-by-step explanation:

Step 1: Equation at the end of step 1

(2²x²+8x)-12

Step 2:

Step 3: Pulling out like terms

Pull out like factors :

4x² + 8x - 12  =   4 • (x² + 2x - 3)

Trying to factor by splitting the middle term

Factoring  x²+ 2x - 3

The first term is,  x²

its coefficient is  1 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   2 .

   -3    +    1    =    -2  

     -1    +    3    =    2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  3

x² - 1x + 3x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-1)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-1)

Step-5 : Add up the four terms of step 4 :

                   (x+3)  •  (x-1)

            Which is the desired factorization

Final result :

Final result :

 4 • (x + 3) • (x - 1)

Now convert to vertex form:

y = 4 (x + 1)² - 16


Related Questions

Which inequality represents this sentence?
A number is at least 65
On < 65
On > 65
On > 65
On < 65

Answers

Answer:

n ≥ 65

Step-by-step explanation:

A number is at least 65. It means the number n can be 65 or greater.

Its translation is:

n ≥ 65

The answer options don't have this included.

Let the number be n

At least 65 means the number is equal to 65 or greater than 65.Hence here we use greater than equal to sign.

Inequality:-

[tex]\\ \sf{:}\Rrightarrow n\geqslant 65[/tex]

can someone help me with this ​

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

Question 1 :

[tex] \sf \sqrt{5 {}^{9} } [/tex]

[tex] \sf{(5 {}^{9} ) }^{ \frac{1}{2} } [/tex]

[tex] \sf {5}^{ \frac{9}{2} } [/tex]Question 2 :

[tex] \sf \dfrac{1}{ \sqrt[3]{12} } [/tex]

[tex] \sf \dfrac{1}{12 {}^{ \frac{1}{3} } } [/tex]

[tex] 12 {}^{ - \frac{1}{3} } [/tex]

Ok done. Thank to me :>

Determine what type of model best fits the given situation: A 4% raise in salary each year. A. none of these B. exponential C. linear D. quadratic ​

Answers

Answer: C. linear

Step-by-step explanation:

Since the raise is going to be a constant amount, a 4% raise, the model will be linear.

Correct me if I am incorrect.

What is the missing angle of the triangle 48° 58°

Answers

Answer:

74 degrees

Step-by-step explanation:

Start w/180 degrees. (The total measure of a triangle.) Then subtract 106 (the sum of the 2 known angles) from 180. We then get 74 degrees (The measure of the missing angle)

omg please help for brainlist !!!!!!!!!!!!!!!!!!!

Answers

Answer:

f(x) is linear

g(x) is exponential

Step-by-step explanation:

A linear function will always have the same rate of change between equally distant points, while an exponential function will have an increasingly large rate of change between equally distant points.

First, look at f(x). All these points are equally distant at 2 units apart on the x-axis, so they can be directly compared:

[tex](-38)-(-18)=-20\\(-58)-(-38)=-20\\(-78)-(-58)=-20[/tex]

All of these points are the same distance apart on the y, so f(x) must be a linear function.

Now look at g(x). These are also all equally distant at only 1 unit apart.

[tex]30-10=20\\90-30=60\\270-90=180[/tex]

These are very clearly not the same distance apart on the y, so g(x) must be the exponential function.

What is the 2nd equivalent fraction to 5/7

Answers

Hello!

2nd equivalent fraction to is 5/7 is 10/14.

Other equivalent fractions are 15/21, 20/28, 50,70...

I hope this helps,

Have a great day!

Which numbers is divisible by 5,10 and 15.

A) 15
B) 20
C) 21
D) 34

Answers

i’m pretty sure it’s 20
We have first find out the factors of the numbers.Factors of 15 are 1, 3, 5, 15.Factors of 20 are 1, 2, 4, 5, 10, 20.Factors of 21 are 1, 3, 7, 21.Factors of 34 are 1, 2, 17, 34.Therefore, there are no numbers in the list, which are divisible by 5, 10 and 15.15 can be divisible by 5 and 15 not 10.20 can be divisible by 5 and 10 not 15.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Please help me with this question

Answers

if any doubt leave a comment

Which of the following values for x will make relation A shown below a function?

A={(3,5),(4,9),(7,2),(x,6)}
A 3
B 4
C 5
D7

Answers

I’m as confused as you are
I think that is is 3

1) WET SURPRISE A water balloon is launched off of a patio. The path of the water
balloon can be modeled by h(t) = -6t2 + 13t + 5, where h(t) is the balloon's height in feet and t is the time in seconds after the balloon is launched.
a. How long will it take for the balloon to splat on the ground?

Answers

The function of the water balloon is an illustration of a quadratic function.

The balloon will splat on the ground after 2.5 seconds

The function is given as:

[tex]h(t) = -6t^2 + 13t + 5[/tex]

When the balloon splats on the ground, the value of h(t) is 0.

So, we have:

[tex]-6t^2 + 13t + 5 = 0[/tex]

Expand the expression

[tex]-6t^2 + 15t- 2t + 5 = 0[/tex]

Factorize the above expression

[tex]-3t(2t - 5)- 1(2t - 5 )= 0[/tex]

Factor out 2t - 5 in the 2t - 5

[tex](-3t - 1)(2t - 5 )= 0[/tex]

Split the equation into 2

[tex]-3t - 1 = 0\ or\ 2t - 5= 0[/tex]

Rewrite as:

[tex]-3t = 1\ or\ 2t = 5[/tex]

Solve for t

[tex]t = -\frac 13\ or\ t = \frac 52[/tex]

The value of t cannot be less than 0 i.e. negative.

So, we have

[tex]t = \frac 52[/tex]

Divide 5 by 2

[tex]t = 2.5[/tex]

Hence, the balloon will splat on the ground after 2.5 seconds

Read more about quadratic functions at:

https://brainly.com/question/11631534

Write an expression that is equivalent to 2 (4x +9)​

Answers

Answer:

8x/3+6 is equivalent and simplified



Write an equation in slope-intercept form of the line that passes through the points (-2.3) and (2.7)

Answers

I'm pretty sure the answer is y=x+5

Please help fast!!!!

Answers

i think it’s 3 not sure!

What point of concurrency in a right triangle is also the midpoint of the hypotenuse?

A. centroid
B. incenter
C. circumcenter
D. orthocenter

Answers

the correct answer is d, i got it right

The point of concurrency in a right triangle is also the midpoint of the hypotenuse is its circumcenter .

What is  point of concurrency?

A point of concurrency is a place where three or more, but at least three lines, rays, segments or planes intersect in one spot. If they do, then those lines are considered concurrent, or the the rays are considered concurrent.

What is Triangle Concurrency Points?

There are 4 different points of concurrency in the triangle are:

1. Circumcenter

The circumcenter is the point of concurrency of the perpendicular bisectors of all the sides of a triangle.

For an obtuse-angled triangle, the circumcenter lies outside the triangle.

For a right-angled triangle, the circumcenter lies at the hypotenuse.

2. Incenter

The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle.

3. Centroid

The point where three medians of the triangle meet is known as the centroid.

4. Orthocenter

The point where three altitudes of the triangle meet is known as the orthocenter.

For an obtuse-angled triangle, the orthocenter lies outside the triangle.

According to the question

The point of concurrency in a right triangle is also the midpoint of the hypotenuse.

According to the Triangle Concurrency Points

For a right-angled triangle, the circumcenter lies at the midpoint of the hypotenuse.

Hence, The point of concurrency in a right triangle is also the midpoint of the hypotenuse is its circumcenter .

To know more about Triangle Concurrency Points here:

https://brainly.com/question/1603917

#SPJ2

[tex]\sf -4(-4x-5)[/tex]

Answers

Answer:

[tex] - 4( - 4x - 5) = - 4 \times - 4x - ( - 4) \times ( - 5) \\ = 16x - 20[/tex]

Answer:

[tex]16x+20[/tex]

Step-by-step explanation:

[tex]-4(-4x-5)[/tex]

[tex]\mathrm{Multiply\:}-4\mathrm{\:to\:the\:values\:in\:the\:parenthesis}[/tex]

[tex]-4(-4x-5)[/tex]

[tex]-4\cdot-4=16[/tex]

[tex]-4\cdot-5=20[/tex]

[tex]=16x+20[/tex]

Type the missing number in this sequence:
-2,

-50,
-250,
-1,250,
-6,250

Answers

Answer:

the next is -2 × 5 = - 10

Step-by-step explanation:

the sequence is times 5

During her vacation, Leslie traveled 578.78 miles in 3 days.


On the first day, she traveled 197.07 miles, and on the second day, she traveled 187.11 miles. how many did she travel the 3rd day?

Answers

Answer:

I think the answer is 194.6 miles on the third day

Step-by-step explanation:

What is 3/10 of 2560

Answers

Answer:

768

3/10 times 2560 simply equals 768 after the calculations are done

(
3.9
×
10

5
)
(
7
×
10

3
)

Answers

Answer:

2278

Step-by-step explanation:

(3.9×10−5)(7×10−3)

= (39 - 5)(7 x 10 -3)

= (39 - 5)(70-3)

= 34(70-3)

= 34 x 67

= 2278

i need help with this!!

Answers

Answer:

12

Step-by-step explanation:

So Josh is 6 years older than kims age and the sum of the ages is less than 31, the greatest number that is less than 31 is 30 so we can use that.

We can make an equation out of this and solve it.

n+(n+6)=30

2n+6=30

2n=24

n=12

12 is the oldest Kim could be.

12+(12+6)=12+18=30.

If the base of the parallelogram is 8 and the perimeter is 28 then what is the area?

Answers

Answer:

the answer is 28 for the area.

Find the first three term if the general nth term is T = 2-n

Answers

Tn = 2n - 6

to find first term ,n= 1

substitute n for 1 in the equation

T1 = 2(1) - 6

T1 = 2 - 6 =-4

to find second term , n =2

substitute n for 2 in the equation

T2 = 2(2) - 6

T2 = 4 - 6 = -2

to find third term, n = 3

substitute n for 3 in the equation

T3 = 2(3) - 6

T3 = 6–6 = 0

FIRST TERM = -4

SECOND TERM = -2

THIRD TERM = 0

-5⎜x - 3⎟ - 5 < 15

Pls

Answers

−5(|x−3|)−5<15

Step 1: Add 5 to both sides.

−5(|x−3|)−5+5<15+5

−5(|x−3|)<20

Step 2: Divide both sides by -5.

−5(|x−3|)

−5

<

20

−5

|x−3|>−4

Step 3: Solve Absolute Value.

|x−3|>−4

We know eitherx−3>−4orx−3<−(−4)

x−3>−4(Possibility 1)

x−3+3>−4+3(Add 3 to both sides)

x>−1

x−3<−(−4)(Possibility 2)

x−3<4(Simplify both sides of the inequality)

x−3+3<4+3(Add 3 to both sides)

x<7

Answer:

x>−1 or x<7

Which graph or graph shows a proportional relationship

Answers

Answer:

C) Graph A and Graph C

Step-by-step explanation:

A proportional relationship has a constant rate of change and goes through the origin. When graphed, the line should be straight and should go through the origin (0,0) as well.

Graph b does not show a straight line so B does not show a proportional relationship.

Graph D shows a straight line but the line does not go through the origin and therefore is not a proportional relationship.

Graphs A and C both show straight lines that go through the origin meaning that they are both proportional relationship.

Thus, the answer is C) Graph A and Graph C

Explain how 3/4 ×7, 7×3/4 and 3×7/4 are all related

Answers

Answer:

3/4×7

= 0.75×7

=5.25

7×3/4

=7×0.75

=5.25

3×7/4

=3×1.75

=5.25

all answer is same so, however we do all answer come 5.25

this way they all are related

-12x - 5y = 40
12x - 11y = 88

Answers

Answer:

(0, -8)

Step-by-step explanation:

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

subtract:-

-5/12 from 2​

Answers

2 5/12 or 29/12

hope it helps ?

study well:)

Answer:  Deopends.  See below.

Step-by-step explanation:

-5/12 from 2​

The question is poorly worded.  Is it asking us to subtract -5/12 from 2?  Or are we being asked to subtract 5/12 from 2?

Assuming the first:

2 - (-5/12)

2 + 5/12

2 5/12 or 24/12 + 5/12 = 29/12

Assuming the second:

2 -5/12

24/12 - 5/12

19/12

What is the product of (6.2*10^4) * (3.4*10^-2)? I got 2,108. am I right?

Answers

Answer:

yes you are right

Step-by-step explanation:

Answer:

Yes, you are right!

Step-by-step explanation:

I hope this helps!

HELP!!!!!
M list the sides of ABC in order from shortest to longest

Answers

Question:

M list the sides of ABC in order from shortest to longest

Answer:

Sum of angles in a triangle = 180

Angles A + B + C = 180

80 + 3x + 5 + 5x - 1 = 180

3x + 5x = 180 - 80 - 5+1

8x = 96

x = 96/8

x = 12

So angle A = 80, B = 3x + 5 = 3*12 + 5 = 36 + 5 = 41, C = 5x - 1 = 5*12 - 1 = 60 - 1= 59

Angle A = 80, B = 41, C = 59

So the smallest side is the side facing the smallest angle and the largest side is the side facing the largest angle.

So from the smallest to biggest side:

AC < AB < BC

Arigatou gozaimasu!!

How many hours is 7:45 to 1:00

Answers

Step-by-step explanation:

There are 17 hours between 7:45 to 1:00

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