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

find the cost of operation of a central air conditioner that uses 3.5 kilowatts and runs for 12 hours a day for one week at a cost of 9.53¢ per kilowatt-hour.

Answers

Answer:2.561,664¢ or roughly 25.61$.

Step-by-step explanation:

So, the air conditioner will cost 3.5 * 9.53 ¢ = 30.496 ¢ per hour running.

That means 30.496¢ * 12 = 365.952¢ or ≈3.65$ for a day.

Or 365.95¢ * 7 = 2.561,664¢ or ≈25.61$ for a week.

I'm vietanh and have fun studying!

Use algebraic notation to describe how to transform the blue function into the red function. F\left(x\right)-1f(x)−1 f\left(x-1\right)f(x−1) f\left(x+1\right)f(x+1) f\left(x\right)+1f(x)+1

Answers

In geometry, transformations are used to move a point or points from one position to another. The notation that describes how the blue function is transformed into the red function is -f(x)

I have attached the graph of both functions.

From the attached graph, we can see that the blue function is reflected over the x-axis to produce the red function.

Let:

[tex]f(x) \to[/tex] Blue

[tex]g(x) \to[/tex] Red

The transformation of reflection across the x-axis is:

[tex]g(x) = -f(x)[/tex]

Hence, the notation that describes how the blue function is transformed into the red function is -f(x)

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The question is "the numbers 4 and 9 both have the exactly three factors, Find two numbers more that have the exactly three factors"

Answers

Answer: 25 and 49

Explanation:

25: 1,5,25
49: 1,7,49

Gwen is attending a school orchestra concert. She sees her math teacher seated 3 meters ahead of her and her science teacher seated 4 meters to her right. How far apart are the two teachers?

Answers

5 metres, using Pythagorean triples as one is infront one is to the right meaning the distance betweent them would create a triangle so u can calculate it to be 5

I need help on number 19 and 20

Answers

Answer:

Explanation:

19.

P = 2(x - 3 + 7x + 1)
= 2(8x - 2)
= 16x - 4

20.

P = 3y + 5 + y - 4 + 6y
= 10y + 1
Number 19: 16x-4

Number 20: 10y +1

7 is the bracket from the quotient of 48 divided by the sum of 5 and difference of 11 and 8​

Answers

6 is supposed to be the bracket

six boys went on a camping trip . their equipment weight was138 kg if the equipment was divided equally in weight how much did each boy carry

Answers

Answer:

138 kg / 6 = 23 kg per boy

Find the area and perimeter.

Hint: The height of a non-right triangle is the length of the segment of a line that is perpendicular to the base and that contains the opposite vertex.

24x; 10x + 8
12x; 7x + 3
24x; 5x + 14
12x; 5x + 14

Answers

Area =a*h/2
Area = 3x*8/2
Area = 12x

Perimeter =a+b+c
a= 8
b=x+9
c= 4X-3
Perimeter =(8)+(x+9)+(4x-3)
Perimeter =8+x+9+4X-3
Perimeter =5x+14
Answer: 12x; 5x+14

The area of triangle will be 12x and perimeter of triangle will be 5x + 14.

The sides of a triangle which is divided into two parts i.e., a right angle triangle and a non-right angle triangle is given in figure.

We have to find area and perimeter of triangle using the data given.

What are the area and perimeter of a triangle ?

The area of triangle is A = [tex]\frac{1}{2}[/tex] × b × h and perimeter is sum of all sides i.e.,  P = a + b + c.

As per the fig. given in question ;

h = 3x

b = 8

The area of the given triangle will be ;

A = [tex]\frac{1}{2}[/tex] × b × h

A =  [tex]\frac{1}{2}[/tex] × 8 × 3x

A = 24x ÷ 2

A = 12x

The perimeter of triangle will be sum of all sides i.e.,

P = x + 9 + 4x - 3 + 8

P = 5x + 17 - 3

P = 5x + 14

Thus , the area of triangle will be 12x and perimeter of triangle will be 5x + 14.

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#SPJ2

What’s the square root of 8
(20 points)

Answers

Answer:

answer is 2

Step-by-step explanation:

can you mark me brainlist

HELP ILL GIVE BRAINLIEST!!

Answers

Answer:

What can I help you with

Answer:

Step-by-step explanation:

Jamie needs 1/5 meter of ribbon to decorate the border of a photo frame. Enter the number of photo frames that can be decorated using 4/5 meter of ribbon​

Answers

Answer:

4 photo frames

Step-by-step explanation:

Hope it will help you

it's 4 pieces of ribbon .

hope it's help you.........!!!!!!!!!!!!!!!!!!!

#rishu

CORRECT ANSWER ONLY PLEASE!!! The table of values represents the function g(x) and the graph shows the function f(x).

Answers

Answer: Choice C.  f(x) and g(x) have a common x intercept.

Explanation:

The graph of f(x) shows it has an x intercept at x = 2, since this is one location where the curve crosses the x axis.

The g(x) table shows that x = 2 and y = 0 pair up together. This is the location (2,0). This location is the exact same x intercept as described earlier.

This is the common x intercept the two functions share. This means the two functions cross or intersect at this location.

Which of the following is false? Explain. A. No integer is an irrational number. B. Every integer is a rational number. C. Every integer is a whole number.

Answers

Answer:

C.

Step-by-step explanation:

integer is a positive and negative number. integer is not a whole number because negative is not part of the whole number.

-4-6 answer now pls iwill mark yall brainliest

Answers

Answer:

-10

Step-by-step explanation:

the answer to the question is-10

Answer:

If it's addition then the answer is

-10

Find the perimeter of a triangle with sides
10 inches, 5 inches, and 11 inches in length.

Answers

Answer:

Answer is D

Step-by-step explanation:

Basically, when finding the perimeter you add up all the sides. So 10 + 5 + 11 which equals 26.

how to do (-5+20) / 5 (-2) / is divide

Answers

Answer:

hope this helps you

have a great day

Answer:

-6

Step-by-step explanation:

(/) is divide right?

[tex]( - 5 + 20) \div 5( - 2)[/tex]

[tex] - 5 + 20 = 20 - 5 = 15[/tex]

[tex]15 \div 5 \times ( - 2)[/tex]

[tex] - (15 \div 5 \times 2) = - (30 \div 5) [/tex]

[tex] = - 6[/tex]

I need help with my homework pls somone help….

Answers

Answer:

x > 9

Step-by-step explanation:

since the dot is open there won't be a line under

write the vertices of each figure​

Answers

Answer:

ABCDE = 5 vertices
PQR = 3 vertices
VWXYZ = 5 vertices
DEFF = 4 vertices

Explanation:

Help please I need that answer rn.Plzz help thanks :))

Answers

Answer:

3 1/3 ÷ 4/5 = 25/6 =4 1/6

Result in decimals: 4.1666666666667

Answer:

The answer is 5/4

For the first expression, 3 multiplies 3 plus 1 divided by the denominator 3

= 3×3 +1÷3

=10/3

then with the second expression, the division sign changes to a multiplication sign . Immediately it changes,4/5 turns to become 5/4

so now it will be

10/3×5/4

=15/12

=5/4

What is the product of ¼, -½ and -¾?

a
0.0934
b
-0.6543
c
-0.09357
d
0.09375

Answers

This is nonfiction and that would c I.09357 0.6543
D most definitely d

601.584 to the nearest tenth

Answers

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Answers

Answer:

Round off to the two decimal places then plot on your Cartesian Plane

in September the digits of the code number are prime factor of 375 what is the code number for the office door in September ​

Answers

Answer:

There are 3 prime factors for 375 (1,3,5)

Step-by-step explanation:

Prime factors are prime numbers meaning they can't be further divided by a whole number.

can someone please help me?

Answers

12 is the answer to this quest

The decimal equivalent of is 3/4 is...

.30

.75

.80

.90

none of these

Answers

Answer:

0.75

Step-by-step explanation:

since it's a fraction you can divide

3 divided by 4 is 0.75

PLEASE HELP Which values of a and b that make the following equation correct?

[tex](2^{a} *3^{2b})^{5} =6^{20}[/tex]

Answers

[tex]\\ \sf\longmapsto (2^a\times 3^{2b})^5=6^{20}[/tex]

[tex]\\ \sf\longmapsto 2^{5a}\times 3^{10b}=(2\times 3)^{20}[/tex]

[tex]\\ \sf\longmapsto 2^{5a}\times 3^{10b}=2^{20}\times 3^{20}[/tex]

On comparing

[tex]\\ \sf\longmapsto 5a=20[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{20}{5}=4[/tex]

And

[tex]\\ \sf\longmapsto 10b=20[/tex]

[tex]\\ \sf\longmapsto b=\dfrac{20}{10}=2[/tex]

Need help pls I will give you 20 more points ASAP

Answers

Step-by-step explanation:

RF (green) = 34/(12+14+34) = 34/60 = 0.57

[tex]\\ \sf\longmapsto RElative\:Frequency(Green)[/tex]

[tex]\\ \sf\longmapsto RF(Green)=\dfrac{34}{12+14+34}[/tex]

[tex]\\ \sf\longmapsto RF(Green)=\dfrac{34}{60}[/tex]

[tex]\\ \sf\longmapsto RF(Green)=\dfrac{17}{30}=0.57[/tex]

Given f(x) = 3x – 1, solve for x when f(x) = -7.

Answers

Answer:

x = -2

Step-by-step explanation:

Given f(x) = 3x – 1

f(x) = -7

3x-1 = -7

3x = -7+1

3x = -6

x = -2

Answer:

x = -22

Step-by-step explanation:

given:

[tex]f(x) = 3x - 1[/tex]

solve for x, when:

[tex]f(x) = -7[/tex]

replace x with -7

~~~~~~~~~~~~

➡️ [tex] x = 3(-7) - 1 [/tex]

➡️ [tex] x = -21 - 1 [/tex]

➡️ [tex]x = -22 [/tex]

The function g is defined by the following rule.
g(x) = 4x-3
Complete the function table.
FASTEST WILL BE MARKED BRAINLIEST

Answers

Plug each x-value into 4x-3.
x=-4: 4(-4)-3 = -16 -3 = -19
x=-2: 4(-2)-3 = -8 - 3 = -11
x=1: 4(1)-3 = 4 -3   = 1

helppppppppppppppppppppppppppppppppppppppppppPp

Answers

Answer:

Step-by-step explanation:

4) You just have to find the lcm of the denominators

a) lcm(4,3,6)=4*3=12

[tex]\dfrac{3}{4} x-\dfrac{2}{3} =\dfrac{1}{6}x\\\\12*(\dfrac{3}{4} x-\dfrac{2}{3}) =12*(\dfrac{1}{6}x)\\\\12*\dfrac{3}{4} x-12*\dfrac{2}{3} =12*\dfrac{1}{6}x\\\\9*x-8 =2*x\\\\9*x-2*x =8\\\\7*x=8\\\\x=\dfrac{8}{7} \\[/tex]

b) I don't know the name of the property but it is :

"We can multiply the two members of an equality by the same non-zero number, we obtain an equality. "

5)

[tex]-6x+10+8x=12-4x\\\\(-6x+10)+8x=12-4x\\\\8x+(-6x+10)=12-4x\\\\8x-6x+10=12-4x\\\\2x+10=12-4x\\....[/tex]

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