can write a quadratic function given key features in the form of ordered pairs

12: Write an equation of each quadratic function, in vertex form, with the given vertex and point

a) Vertex at (1.2) and passes through the point (3.4)

b) Vertex at (-5, -1) and passes through the point (6.3)

Answers

Answer 1

Answer:

ANSWER IS BELOW

Step-by-step explanation:

f

(

x

)

=

1

2

x

2

+

3

x

1

2

Explanation:

A quadratic function can be written in vertex form as:

f

(

x

)

=

a

(

x

h

)

2

+

k

where

(

h

,

k

)

is the vertex and

a

is a constant multiplier.

In our example the vertex

(

h

,

k

)

is

(

3

,

4

)

, so we can write:

f

(

x

)

=

a

(

x

3

)

2

+

4

Given that this passes through the point

(

1

,

2

)

, we must have:

2

=

a

(

1

3

)

2

+

4

=

4

a

+

4

Subtract

4

from both ends to get:

2

=

4

a

Divide both sides by

4

and transpose to find:

a

=

1

2

So our quadratic function can be written in vertex form as:

f

(

x

)

=

1

2

(

x

3

)

2

+

4

We can multiply this out and simplify as follows:

f

(

x

)

=

1

2

(

x

3

)

2

+

4

f

(

x

)

=

1

2

(

x

2

6

x

+

9

)

+

4

f

(

x

)

=

1

2

x

2

+

3

x

9

2

+

4

f

(

x

)

=

1

2

x

2

+

3

x

1

2


Related Questions

I will try to give branliest
The data set shows the number of players on each softball team in a tournament:

9

12

8

7

7

21

11

9

8

7

10

7

10

11



Which of the following statements is true based on the data set? (4 points)

There is one outlier that indicates an unusually large number of players on that team.
There are two outliers that indicate an unusually large number of players on those two teams.
There is one outlier that indicates an unusually small number of players on that team.
There are two outliers that indicate an unusually small number of players on those two teams.

Answers

Answer:

it is B, there is one big outlier, it is 21

Step-by-step explanation:

Solve the equation 4(z−3)=2z9+22 using the balancing method.
z=

Answers

Answer:

z = 9

See my attachment below for step-by-step explanation.

solve for variable. 3p/5 + 8/5 =1

Answers

[tex]\\ \sf\longmapsto \dfrac{3p}{5}+\dfrac{8}{5}=1[/tex]

[tex]\\ \sf\longmapsto \dfrac{3p+8}{5}=1[/tex]

[tex]\\ \sf\longmapsto 3p+8=5[/tex]

[tex]\\ \sf\longmapsto 3p=5-8[/tex]

[tex]\\ \sf\longmapsto 3p=-3[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{-3}{3}[/tex]

[tex]\\ \sf\longmapsto p=-1[/tex]

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!
URGENT!!!!!!!

For the function h defined by h(x)=2x^2 − 2, find h(0).

Answers

Answer:

h(0) = - 2

Step-by-step explanation:

Substitute x = 0 into h(x) and evaluate , that is

h(0) = 2(0)² - 2 = 2(0) - 2 = 0 - 2 = - 2

Solving equations and inequalities.

I’m confused on the subtraction behind the one, am I supposed to turn the one into a negative?

1-(4+3x)<-3

Answers

Answer:

x>0

Answer to your question:

Because the subtraction sign is after the negative, it applies to the term in front of it, in this case because there is a parenthesis, it would multiply into that and your equation from there would be 1-4-3x<-3. Then combine like terms from there.

p 2 + m; use m = 1, and p = 5

Answers

Answer:

26

Step-by-step explanation:

p²+m

=> 5²+1

=> 25 + 1

=> 26

Answer:

26

Step-by-step explanation:

Substitute the given values into the expression

p² + m

= 5² + 1

= 25 + 1

= 26

How much time has passed from the first clock to the second clock?
The time passed is less than 12 hours. 4:20 and 8:55

Answers

I believe 4 hours and 35 minutes has passed.

ASAP PLS

1. Using the figure below to answer the question. If the sector (APB) has an area of 7pi and m<APB = 44°, find the radius length for circle P. (answer choices are 6.35, 9.27, 7.57, and 9.7)​

Answers

Answer:

7.57

Step-by-step explanation:

the area = 44/360 × π × r²

7 π = 44/360 × π× r²

eliminate π

7 = 44/360 x r²

r² = 7× 360/44

r² = 57.27

r =√57.27 = 7.57

Using the segment addition postulate find the length of the segment EF

Answers

Answer:

10

Step-by-step explanation:

I'm pretty sure the segment addition postulate just means that if you add JK and KL together, you'll get the length of JL. Correct me if I'm wrong...

Anyways, JK = 3x - 4, and KL = 5x + 6. If we add these together, according to the segment addition postulate, we will get JL, which equals 9x - 8. So, we set up an equation:

3x - 4 + 5x + 6 = 9x - 8

Simplifying this equation, we get:

8x + 2 = 9x - 8

x = 10

So, our answer is 10.

(also you ask for segment EF but I don't see segment EF so I'm going to just answer the question in the picture)

Simplify: (14^6*15^5)/(35^6*6^5)​

Answers

Answer:

2/5

Step-by-step explanation:

=(2*7)^6 * (3*5)^5/ (7*5)^6 * (2*3)^5

=(2^6 * 7^6) * ( 3^5 * 5^5) / (7^6 * 5^6) * ( 2^5* 3^5)

=2^5 * 2^1 * 5^5/ 5^5 * 5^1 *2^5

=2/5

The simplified expression of (14^6*15^5)/(35^6*6^5)​ is 2/5

How to simplify the expression?

The expression is given as:

(14^6*15^5)/(35^6*6^5)​

Express 14 as 2 * 7, 15 as 3 * 5 and 35 as 5 * 7

[tex]\frac{(2 * 7)^6 * (3 * 5)^5}{(5 * 7)^6 * (2 * 3)^5}[/tex]

Expand the expression

[tex]\frac{2^6 * 7^6 * 3^5 * 5^5}{5^6 * 7^6 * 2^5 * 3^5}[/tex]

Divide the common factors

[tex]\frac{2}{5 }[/tex]

Rewrite as:

2/5

Hence, the simplified expression of (14^6*15^5)/(35^6*6^5)​ is 2/5

Read more about expressions at:

https://brainly.com/question/4344214

2
614
eft
3.
9m
Please help

Answers

2.

[tex] area=\frac{1}{2} \times 6 \times 8 \\ = 24 [/tex]

3.

[tex]area = \pi \times 9m \\ = 3.14 \times 9 \\ = 28.26 {m}^{2} [/tex]

Solve for x: −3x − 3= −3(x + 1)

Question 4 options:

All real numbers


No solution


6


−6

Answers

Answer:

all real numbers

Step-by-step explanation:

The equation of x has No solution.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

−3x − 3 = −3(x + 1)

Expanding the brackets we get,

−3x − 3 = −3x − 3

Collecting like terms together we get,

−3x +  3x = −3 + 3

Solving we get,

0 = 0

So, this equation has no solution.

Thus, the equation of x has No solution.

To learn more about equations here :

https://brainly.com/question/14427555

#SPJ2

jskaoqlqmsbdnsoqqk
[tex] \sqrt{5} \times \sqrt{15} \times \sqrt{3} [/tex]

Answers

Answer:

[tex] \sqrt{5} \times \sqrt{15} \times \sqrt{3} \\ \\ \sqrt{5 \times 15 \times 3} \\ \\ = 5 \times 3 \\ \\ = 15[/tex]

[tex]\\ \rm\longmapsto \sqrt{5}\times \sqrt{15}\times \sqrt{3}[/tex]

[tex]\\ \rm\longmapsto \sqrt{5\times 15\times 3}[/tex]

[tex]\\ \rm\longmapsto \sqrt{5\times 5\times 3\times 3}[/tex]

[tex]\\ \rm\longmapsto 5(3)[/tex]

[tex]\\ \rm\longmapsto 15[/tex]

A number of tourist were interviewed on their
choice of
means
of travell Two-thirds said
they had travel by road, 13 by air. 4
the by
both
air and road. If
20 tourist had not travel
road
Represent the information on
on a Vena
diagram:
by either
air
or road. Represent the information on a venn diagram​

Answers

Answer:

A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, 1330 by air and 415 by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?

help me plzzzzzzzzzzz ​

Answers

Answer:

x = 18°

Step-by-step explanation:

∠AOB and ∠BOD form linear pair of angles, so they are supplementary, i.e., their sum is 180°.

130° + (2x + 14)° = 180°

=> 130° + 2x° + 14° = 180°

=> 2x° = 180° - 130° - 14°

=> 2x° = 36°

=> x = 36°/2°

=> x = 18°

x=18 degrees


I hoped this helped

Which option is the correct interpretation of this numerical expression?
55 ÷ 5 − 4

the quotient of 55 divided by 5, decreased by 4

four subtracted from the product of 55 and 5

five less than the quotient of 55 divided by 4

fifty-five divided by the difference of 5 and 4

Answers

Answer:

7

Step-by-step explanation:

bc 11×5=55 so you divide it and its 11-4=7 :)

Question 4 of 30
Find the probability of rolling two dice and getting 2's on both.
.
A. 1/60
B. 1/30
C. 1/2
D.1/36
HELP ASAP

Answers

Answer:

1/36

Step-by-step explanation:

prob of each dice is 1/6

=1/6 * 1/6

Help please and please explain how I don’t understand

Answers

Use Pythagoras
x^2 = 6^2 + 12^2 = 36 + 144 = 180
x = sr(180) = 13.42 in (4 s.f.)

Number x is 10% more than number y. Number y is 10% more than number z. How much percent is number z less than number x?
pls step by step​

Answers

Answer:

i hope it helped U

stay safe stay happy

Calculate the diameter of a
circle if its area is 113.1cm2.

Answers

Answer:

12 cm squared

Step-by-step explanation:

1. Since diameter is twice the radius and what we know is the area, you would divide the area, 113.1 cm, by Pi (3.14):

113.1 cm / 3.14 = 36.00084813

2. What you get is the radius which you have to square:

36.00084813 squared = 6.000070677

3. Now you double the radius in order to get the diameter:

6.000070677 x 2 = 12.00014135

12.0 cm squared

what is equivalent to -7/-9

Answers

-7/-9 is equivalent to -14/-18. Multiply the denominator and numerator by the same number(I used 2)

please help fassttttt​

Answers

Answer:

Step-by-step explanation:

h = 20 + 1.7 + 50 = 71.7 m

Which polynomial is in standard form?
O 2xy + 3x8y4 - 4x4y5 + 9x576
O 8X5 - 5y4 – 2xy + xy
O x3y2–3x2y-9x4y +11x
O 5x?y2 +7x8y5 – 14x3y? +51x2y9

Answers

The polynomial in standard form is as follows;

8x⁵  - 5y⁴ - 2xy⁵ + x²y

How to find the standard form of polynomial?

A polynomial can have constants, variables and exponents, but never division by a variable. example of a polynomial is as follows:

4xy² + 2y + 5

Polynomial can be named base on the number of terms. For example monomial, binomial and trinomial.

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Therefore, the polynomial in standard form is as follows;

8x⁵  - 5y⁴ - 2xy⁵ + x²y

learn more on polynomial here: https://brainly.com/question/27205112

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Answer: its b

8xy5 -5y4 -2xy5 +x2y

Step-by-step explanation:

I got it right on edge

I neeed helppp please due today

Answers

Step-by-step explanation:

y=x+6.......(1)

y=-3X-6....(2)

from eq (1), we get,

x=y-6....(3)

sub eq (3) in eq (2), we get

y= -3(y-6)-6

y= -3y+18-6

y+3y-12=0

4y=12

y=3

sub value of y in eq (3)

x=3-6

x=-3

Answer: (3, 3)

Step-by-step explanation:

There are three general ways of solving a system of equations:

EliminationSubstitutionGraphing

When solving systems of equations with graphing, look for points that overlap with each other or cross, and that will be the solution for the system. There might be one, two, or more than two solutions.

Please refer to the attachment below for the graph of the two equations.

Red line: y = x + 6Blue line: y = -3x - 6

Hope this helps!! :)

Please let me know if you have any questions

Which of the following shows the given inequality as an equivalent inequality in which the inequality symbol points in the opposite direction?
8 - 2<8
O 2 <8-2
O 8 > 8 + 2
O2 <2 - 8
08>8 - 2
O 8 = 8 - 2

Answers

Answer:

8 > 8 - 2

Step-by-step explanation:

because that is just the other side of the same "coin".

8 - 2 < 8

data exactly the same thing as

8 > 8 - 2

Given f(x)=2x^2+3x-8 find (b+2)

Answers

Answer:

[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = 2x^2 + 3x - 8[/tex]

And we want to find:

[tex]\displaystyle f(b + 2)[/tex]

Substitute:

[tex]\displaystyle f(b+2) = 2(b+2)^2 + 3(b+2) - 8[/tex]

Expand and simplify:

[tex]\displaystyle \begin{aligned}f(b+2)&= 2(b^2+4b+4)+(3b+6)-8 \\ &= (2b^2+8b+8)+(3b+6)-8 \\ &= (2b^2) + (8b+3b)+ (8+6-8) \\ &= 2b^2 + 11b + 6 \end{aligned}[/tex]

In conclusion:

[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]

8x - 5y = 74
What is y and x?

Answers

Answer:

x = 11/2

   y = -x/2+35/4

Step-by-step explanation:

Help help help help help help help help help help help plss

Answers

Answer:

$48.

Step-by-step explanation:

60% off

= 120 - 0.60*120

= 120 - 72

= $48.

I think it’s 72 sorry if I am wrong

how much time will it take for a bug to travel 5 meters if it is traveling 1 m/s

Answers

Answer:

5

Step-by-step explanation:

divide the distance by the rate of speed

5/1=5

Answer:

5 seconds.

Step-by-step explanation:

The product of two whole numbers is 10000. If neither of the numbers contains a digit of 0, then what is their sum?

Answers

Step-by-step explanation:

we should add 9999 add 1

it is the answer of this qp

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