What is the vertex of the parabola with the equation y
3x2 + 2x – 8?

Answers

Answer 1

Answer:

Step-by-step explanation:

If you're tasked to do this mathematically, you have to complete the square to get it into vertex, or work, form. Do that by first setting the equation equal to 0 then moving over the constant:

[tex]3x^2+2x=8[/tex] Next you have to have a +1 as the leading coefficient, and ours is a 3, so we factor it out:

[tex]3(x^2+\frac{2}{3}x)=8[/tex]. Now take half the linear term, square it, and add it in to both sides. Our linear term is 2/3. Half of 2/3 is 2/6 which reduces to 1/3. Squaring 1/3 gives us 1/9, so that's what we add in.

[tex]3(x^2+\frac{2}{3}x+\frac{1}{9})=8+\frac{1}{3}[/tex] to the right of the equals sign we added in 3*1/9 which is 3/9, which reduces to 1/3. Now we clean up both sides. The right side is easy; the left side, not so much. The reason we do this (complete the square) is to get a perfect square binomial on the left. When we re-write the left side into that perfect square binomial, we get

[tex]3(x+\frac{1}{3})^2=\frac{25}{3}[/tex] Now we move the constant back over and set the parabola back equal to y:

[tex]y=3(x+\frac{1}{3})^2-\frac{25}{3}[/tex] which shows us that the vertex is

[tex](-\frac{1}{3},-\frac{25}{3})[/tex]


Related Questions

EG is the angle bisector of

Answers

Answer:

the remaining angle will be 32

cz angle bisector cuts an angle in two equal parts hooe it may help u

If α and β are the zeroes of the polynomial ax^2 + bx + c, find the value of α^2 + β^2

Answers

Answer:

Step-by-step explanation:

α + β = -b/a

αβ = c/a

α² + β² = (α + β)² - 2αβ

           [tex]= (\frac{-b}{a})^{2}-2\frac{c}{a}\\\\= \frac{b^{2}}{a^{2}}-\frac{2c}{a}\\\\=\frac{b^{2}}{a^{2}}-\frac{2c*a}{a*a}\\\\=\frac{b^{2}-2ca}{a^{2}}[/tex]

I need help with this plz

Answers

Answer:

[tex]x^{15}[/tex]

Step-by-step explanation:

Distribute the ^3 on top

(27 [tex]x^{6}[/tex] [tex]y^{-9}[/tex])

distribute the ^ -9 on bottom, only to what is in the parenthesis

(27 [tex]x^{-9}[/tex] [tex]y^{-9}[/tex])

the 27's cross out, the [tex]y^{-9}[/tex] 's cross out

[tex]x^{6}[/tex]/ [tex]x^{-9}[/tex] is left

move the  [tex]x^{-9}[/tex] to the top of fraction to change its sign

[tex]x^{6}[/tex] · [tex]x^{9}[/tex] = [tex]x^{15}[/tex]

A bus completed a journey of 98 km in 140 minutes. Calculate the average speed, in kilometres per hour, for this journey.​

Answers

Answer:

hope you like it

Step-by-step explanation:

at first change minutes to hour and calculate by dividing 98 to specific hour

Speed=distance/time

-change time from minutes to hours:
140= 2hours 20= 2.333

Speed=98/2.333
= 42 km/h

I think?

AC and DG are parallel. Find the value of x, show CLEARLY how you got your answers with reasons

Answers

Answer:

x = 79°

Step-by-step explanation:

∠ABE = ∠BEF  = 41°           [Alternate angle ]

Now sum of angles of a triangle = 180°

Therefore,

∠EBF + ∠BEF + ∠BFE = 180°

60° + 41° + x = 180°

x = 180° - 60° - 41°

x = 79°

A 3 by 3cm grid shows nine 1 by 1 cm squares and uses 24cm of wire.

What length would the wire be for a similar 20 by 20cm sqaure

Answers

Answer:

840 cm

Step-by-step explanation:

Given that in the question we have, : 9, 1 cm × 1 cm squares setting a 3 × 3 grid.

Therefore wire required in 3 x 3 grid is

3(3+1) + 3(3+1)

= 3 × 4 + 3 × 4

= 24 I'm

Similarly, the length of the wire required in 20 by 20 grid will be

=> 20(20+1) + 20(20+1)

=> 20 × 21 + 20 × 21

=> 420 + 420

= 840cm

please complete the table.

Answers

Answer:

my answer in this picture.......

what is 11010^2 - 1101^2​

Answers

Answer:

-120,007,899

Step-by-step explanation:

Given :

[tex]11010^{2} -1101^{2}[/tex]

It can be solved as :

[tex]11010^{2} -1101^{2}[/tex]

121,220,100-1212201

-120,007,899

Therefore, answer will be -120,007,899

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

[tex]\mathsf{11,010^2 - 1,101^2}[/tex]

[tex]\mathsf{11,010^2}[/tex]

[tex]\mathsf{= 11,010 \times 11,010}[/tex]

[tex]\mathsf{= \boxed{\bf 121,220,100}}[/tex]

[tex]\mathsf{\bold{121,220,100} - 1,101^2}[/tex]

[tex]\mathsf{1,101^2}[/tex]

[tex]\mathsf{= 1,101 \times 1,101}[/tex]

[tex]\mathsf{= \boxed{\bf 1,212,201}}[/tex]

[tex]\mathsf{121,220,100 - \bf 1,212,201}[/tex]

[tex]\mathsf{= \boxed{\underline{\bf 120,007,899}}}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \underline{\bf 120,007,899}}}}\huge\checkmark[/tex]

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

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

a bicycle was sold for $285 at a discount of 5% calculate the cost price of that bicycle​

Answers

270.75$ is the price of the bicycle

Answer:

Cost price = $300

Step-by-step explanation:

Let the cost price be = x

Discount % = 5%

Price after discount = $285

Find Cost price .

 [tex]Price \ after \ discount = x - (5 \% \ of \ x)\\\\285 = x - \frac{5}{100}x\\\\285 = \frac{100 - 5 }{100} x\\\\95x = 285 \times 100\\\\x = \frac{28500}{95} = \$ 300[/tex]

35 into binary number

Answers

Answer:

35 in binary is 100011.

Step-by-step explanation:

To find decimal to binary equivalent, divide 35 successively by 2 until the quotient becomes 0.

The number 35 in binary form should be 100011

Question 7 of 10 Classify the following triangle. Check all that apply. 6 D A. Scalene D B. Right C. Obtuse D. Isosceles E. Acute F. Equilateral​

Answers

Answer:

Right angle triangle

Acute

Step-by-step explanation

1 right angle/90 degrees

2 acute angles

A bag contains 26 letters and 10 numerals. Robin draws two cards from the
bag. What is the probability that she draws 2 numerals?

Answers

Answer:

10C2 / (36C2)

Step-by-step explanation:

First card = 10/36
Second card= 9/35
Probability that both numerals= 10/36 x 9/35
= 1 / 14

Help me plssss? Thanks

Answers

Answer:

B

Step-by-step explanation:

Simplify......................​

Answers

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{( {a}^{2} + {b}^{2} )}{a} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{ {a}^{4} - {b}^{4} }{ {a}^{3} - a {b}^{2} } [/tex]

[tex] \\= \frac{ ({ {a}^{2} })^{2} - { ({b}^{2} })^{2} }{a( {a}^{2} - {b}^{2} )} [/tex]

[ ∵ (a²)² = [tex]{a}^{4}[/tex] ]

[tex] \\= \frac{( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2}) }{a( {a}^{2} - {b}^{2}) } [/tex]

[tex] \\= \frac{( {a}^{2} + {b}^{2} )}{a} [/tex]

Note:

[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{ヅ}}}}}[/tex]

i cant do this lollllllll

Answers

The answer would be 6. When you do the parentheses, it gives you 3. 3 squared is 9, which added with 9 is 18. 18 divided by 3 is 6.

Answer:

12

Step-by-step explanation:

first, do the question in parenthesis

then do the questions in the exponent

then do the question with division

then do addition part

(7-4)^2 = (3)^2

9/3 = 3

9+3 = 12

Which of the following is a geometric sequence?
O A. -2, 6, 14, 22, ...
O B. 6, 13, 19, 24, ...
O c. 11, 16, 21, 26, ...
O D. -3,3, -3, 3, ...

Answers

Answer:

O B. 6, 13, 19, 24,

Step-by-step explanation:

because this is the correct answer

The answer would be D as it’s the only one with a scale factor which is multiplying by -1

April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs.

What is the complement of April choosing five pop CDs?

choosing five CDs where none of them are pop
choosing five CDs where not all of them are pop
choosing five CDs where at least one of them is pop
choosing five CDs where all of them are pop

Answers

Answer:

Choosing five CDs where not all of them are pop.

Step-by-step explanation:

Answer:

B)  choosing five CDs where not all of them are pop

Step-by-step explanation:

E2020

Please help me with this question.

Answers

Answer:

[tex]80\text{ square miles}[/tex]

Step-by-step explanation:

Since the map is using a scale of 1 inch : 5 miles, to find the scale of square inches to square miles, square the ratio:

[tex]\implies 1\text{ square inch}:25\text{ square miles}[/tex]

Since the section of land has an area of 3.2 square inches, the actual area of the section of land must be [tex]3.2\cdot 25=\boxed{80\text{ square miles}}[/tex]

Which table shows a proportional relationship between a and b?
A.
a b
3 9
4 12
5 20
B.
a b
20 25
24 30
32 40
C.
a b
4 12
5 15
6 24
D.
a b
3 4
6 9
12 16

Answers

B I think I’d the answe

what is the value of the expression below?​

Answers

Answer:

C

Step-by-step explanation:

Using the rule of exponents/ radicals

[tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex] , then

[tex]121^{\frac{1}{2} }[/tex] = [tex]\sqrt{121}[/tex] = 11 → C

The seventh term of an arithmetic series is 29 and the sum of the first seventeen terms is 629. Find the sum of the first 100 terms of the series.

Answers

Step-by-step explanation:

everything can be found in the picture

Help pleaseeeeeeeeeeeeeeeeeeeeee

Answers

Answer: x= -7/8

Step-by-step explanation:

Hope it helps you

I need help!!! Parallel lines p and q are cut by two non parallel lines m and n as shown in the figure the value of x is degrees and the value of y is degrees

Answers

Answer:

x = 78° , y = 115°

Step-by-step explanation:

The angle adjacent to x on the left side is corresponding to 102° , then

x = 180° - 102° = 78°

----------------------------------------

y and 115° are corresponding angles and congruent, then

y = 115°

There is 28 kg 750 g of sugar in a sack. How many tins of 500 g sugar can be filled using the sugar in the sack?

Answers

Answer:

Step-by-step explanation:

28 kg + 750 g = 28*1000 + 750

                          28000 + 750

                       = 28750 g

Number of sack = Total quantity of sugar ÷ quantity of sugar in a sack

                           = 28750 ÷ 500

                           =  57 sacks

Answer:

57 sacks

Step-by-step explanation:

28750 ÷ 500 =

57 sacks

Glad to help! :)

Consider the system of equations: Equation 1: -2x + 3y=9 Equation 2 : -8.1 – 7y = 10 Before adding the equations together, which would not result in the elimination of the variables in this system? Multiply the first equation by 8 and the second equation by 2. O Multiply the first equation by 7 and the second equation by 3. O Multiply the first equation by 4 and the second equation by -1. o Multiply the first equation by 14 and the second equation by 6.​

Answers

The first option :

Multiply the first equation by 8 and the second equation by 2

would not result in the elimination of the variables in this system

please helpppp its due nowwwww

Answers

Answer:

Step-by-step explanation:

instead of (2x - 60 ) there should be (60 - 2x) because since they are parallel lines corresponding sides must be equal . It is contradictory because the size of the corresponding angles is different.

Note : Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

consider the system of equations given below
Y=2/3x+2
Y=5/2x+7/2
which of the following is true about the solution set of the system?
A. The solution is a point on the x-axis.
B. The solution is all the points on the line y=2/3x+3.
C. The solution is a point in the coordinate plane.
D. The solution is the region in the coordinate plane above y=5/2x+7/2.

Answers

Answer:

its A or C

Step-by-step explanation:

The manned is a powerful force in a free market and 3 to 4 cents and fling some of the factors that cause changes in demand and why it is important for consumer standards and the changes

Answers

Answer:

The description as per the given question is provided below.

Step-by-step explanation:

Demand reflects a shareholder's intent to attract consumers as well as works as a gauge of such a buyer's ability to collect a particular preference for a particular commodity.

The factors that change the demand are as follows:

User needs as well as requirements.Changes affecting associated commodity prices.Peoples' political revenues.The general economy's proportion of participants.

14. A polygon ABCD is inscribed in a circle. Find angle ABC

15. A polygon GHIJ is inscribed in a circle if GHI=76 and HIJ=66 what is IJG

Answers

Answer:

m<ABC = 100degrees

m<IJG = 104degrees

Step-by-step explanation:

14. The sum of the opposite angle of the quadrilateral is 180degrees. Hence;

m<ADC + m<ABC = 180

3y+8+4y+4 = 180

7y + 12 = 180

7y = 180 - 12

7y = 168

y = 168/7

y = 24

Get <ABC

m<ABC  = 4y+4

m<ABC = 4(24) + 4

m<ABC = 96 + 4

m<ABC = 100degrees

15. Similarly for this;

GHI + IJG = 180

76 + m<IJG = 180

m<IJG = 180 - 76

m<IJG = 104degrees

Which is equivalent to 80
?
80
4
V80*
O 809
80
o
what is equivalent to 80 1/4?

Answers

The answer is 4 square root 80
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