Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept: (0,1)

Answers

Answer 1

Answer:

y = (1/4)x² - (5/4)x + 1

Step-by-step explanation:

The x-intercepts of the quadratic equation are simply it's roots.

Thus, we have;

(x + 1) = 0 and (x - 4) = 0

Now, formula for quadratic equation is;

y = ax² + bx + c

Where c is the y intercept.

At y-intercept: (0,1), we have;

At (-1,0), thus;

0 = a(1²) + b(1) + 1

a + b = -1 - - - (1)

At (4,0), thus;

0 = a(4²) + b(4) + 1

16a + 4b = -1

Divide both sides by 4 to get;

4a + b = -1/4 - - - (2)

From eq 1, b = -1 - a

Thus;

4a + (-1 - a) = -1/4

4a - 1 - a = -1/4

3a - 1 = -1/4

3a = 1 - 1/4

3a = 3/4

a = 1/4

b = -1 - 1/4

b = -5/4

Thus;

y = (1/4)x² - (5/4)x + 1


Related Questions

Someone please help me with this math problem?

Answers

Answer:

(C) 0.3(10 + 4h) = 0.25(6h)

Step-by-step explanation:

Here's what we know about Fernando's fees:

$10 is the initial fee

$4 is the hourly fee (h)

Saves 30% (also written as 0.3) of the total cost (includes initial and hourly fee)

Here's what we know about Brenna's fees:

No initial fee

$6 is the hourly fee (h)

Saves 25% (also written as 0.25) of the total cost (just the hourly fee because she doesn't have an initial fee)

We want to find which hour Fernando and Brenna will have saved the same amount of money.

To do this, let's first set up an equation for Fernando and Brenna separately:

Fernando's equation:

0.3(10 + 4h) = how much money he saves from the total cost

Brenna's equation:

0.25(6h) = how much money she saves from the total cost

Now we set them equal to each other:

0.3(10 + 4h) = 0.25(6h)

There's your answer!

Hope it helps (●'◡'●)

Help, someone please lol

Answers

Answer:

2x+5x^2=1

2x+5x*5x=1

2x+25x=1

27x=1

1/27=x

Hope This Helps!!!

Answer:

D. 24

Hope it helps!

If px-3+qx+1=2x+3,Find the value of p+q

Answers

Answer: p + q = (2x+5)/x

isolate p + q on one side: therefore rewrite the equation.

px + qx -2 = 2x + 3

px + qx = 2x + 5

x(p+q) = 2x+5

p + q = (2x+5)/x

Express y in terms of x in the equation ax + by = c where b is not equal to zero.

HELLLP

Answers

Answer:

y=(-ax+c)/b

Step-by-step explanation:

ax+by=c

by=c-ax

by=-ax+c

y=(-ax+c)/b

A lunch menu consists of 2 types of tortillas and 5 different fillings. How many choices are there for ordering a burrito with one filling?

Answers

Answer:

You can choose between 10 different choices.

Step-by-step explanation:

Given that a lunch menu consists of 2 types of tortillas and 5 different fillings, to determine how many choices are there for ordering a burrito with one filling, the following calculation must be performed:

2 x 5 = X

10 = X

Therefore, you can choose between 10 different choices.

Between 20 to 35 degrees north latitude, and also between 20 to 35 degrees south latitude are found:

Answers

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Its area includes all Sahara's locations in North Africa, South Arabia, Iran's and Iraq's larger parts, North-Western India, California throughout the United States, South Africa but most of Australia.

Half-arid temperatures include places like the Utah, Montana, and Gulf Coastal regions of sagebrush. Also, it comprises regions in Iceland, Russia, Scandinavia, Greenland, and Northeast India. Semi-arid thankless than tube called per year of rain and up to 20 inches per year at much more than arid deserts.

Regions from of the latitude of 25° to 35° usually develop desert, because air sinks and is heated under pressures in this area. The world's dry and semi-arid desert regions are between 20°C and 35°C north latitude and between 20°C and 35°C South latitude.

PLEASE HELP! Which of the following ordered pairs is a solution to the given system of equations?

A. (12, 8)

B. (3, 5)

C. (-3, 3)

D. (0, 4)

Answers

Answer:

A number has to be the answer

Given the function f(x) = -5|x + 1 + 3, for what values of x is f(x) = -12?
O x = -2x = 4
O x = -2, x = 4
O x = 2, X= 4
O x= 2 X= 4

Answers

F(x) = - 5(x+1+3)

or, - 12= - 5x-5-15

or, - 12= - 5x-20

or, - 12+20= - 5x

or, 8= - 5x

or, x= 8÷-5

Also,

F(x)= - 5(x+1+3)

or, f(8÷-5)= - 5(8÷-5+1+3)

= - 5(8-5-15÷-5)

= - 5×-12÷-5

= - 12 #

Match the base to the corresponding height.

Answers

Answer:

I can't see the picture

Step-by-step explanation:

SORRY :(

Q2: 8,15,22,29,36,............ A sequence of numbers is shown above. a) Find the 10th term of the sequence. *

This is a required question
b) Find the nth term of the sequence. *
c) Which term of the sequence is equal to 260. *

Answers

Answer:

a) 71

b) an = a1 + (n-1)×7

c) the 37th term

Step-by-step explanation:

clearly, an+1 = an + 7

so, any new term is the previous term plus 7.

a1 = 8

and then the sequence goes on. starting with a2 we add 7 every time.

so, for an we added 7 n-1 times to a1. n-1 because for a1 we did not have to add 7.

therefore, the building function of this sequence to calculate the nth term is

an = a1 + (n-1)×7

a10 = a1 + 9×7 = 8 + 63 = 71

and

ax = 260 = a1 + (x-1)×7 = 8 + 7x - 7 = 1 + 7x

259 = 7x

x = 37

=> the 37th term of the sequence is 260

a) 71
b) an = al + (n +1) x 7
c) 37th term

What is X if
[-1 -2] +X = [-5 -1]
[4 8] [ 2 1]

A)
[-6 -3]
[6 9]

B)
[-6 -3]
[-2 -7]

C)
[-4 1]
[-2 -7]​

Answers

Answer:

I think that ans is A.....

someone please help!!

Answers

Reflection, the quadratic parent function is reflected on the opposite side

Find x from this triangle

Answers

Hello,

we are going to use the theorem of the bissectrice. (if this word is good in english)

[tex]\dfrac{KL}{LM} =\dfrac{KN}{NM} \\\\\dfrac{8}{x} =\dfrac{14}{20-x} \\\\8(20-x)=14x\\\\160-8x=14x\\\\22x=160\\\\x=\frac{160}{22} \\\\x=\frac{80}{11} \\\\\\x=7.\overline{27}[/tex]

I need help. Someone please figure it out

Answers

Answer:

[tex]\frac{1}{2^{n} }[/tex]

Step-by-step explanation:

The rules of exponents state that

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] and [tex]a^{0}[/tex] = 1

Thus

[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]

[tex]2^{-4}[/tex] = [tex]\frac{1}{2^{4} }[/tex] = [tex]\frac{1}{16}[/tex]

[tex]2^{-3}[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

and so on , to

[tex]2^{0}[/tex] = 1


Solve for x, then choose
the correct graph.
- 3x > 12

Answers

answer:

-4

Step-by-step explanation:

-3x>12

x<-4

the correct graph is graph b

If you added 74 and 5/8, would the answer be more than 12, less than 12, or
exactly 12? How do you know?

Answers

Answer:

more than 12

Step-by-step explanation:

because one of the numbers is already larger than 12

The sum of two numbers is 50. The larger number is 20 more than the smaller number. What are the numbers? ​

Answers

Answer:

the smaller number is 15 and the larger number is 35

Step-by-step explanation:

x+y=50

x=smaller number y=larger number

y=x+20

x+(x+20)=50

2x+20=50

2x=30

x=15

smaller number=15

larger number= 15+20=35

Answer:

Smaller: 15

Larger: 35

Step-by-step explanation:

1. Finding the two equations

Larger: y

Smaller: x

[tex]x+y=50[/tex]

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

2. Plugging it in

[tex]x+20+x=50\\2x=50-20\\2x=30\\x=15[/tex]

[tex]15+y=50\\y=50-15\\y=35[/tex]

x=15; y=35

Hope this helped! Please mark brainliest :)

question in picture, math.

Answers

Answer:

beginning of march 4.1

beginning of jun      6.4

Step-by-step explanation:

If 2.2 pounds = 1 kilogram and Mary weighs 120 pounds, how much does she weigh in
kilograms?

Answers

Given:

2.2 pounds = 1 kilogram

Weight of Mary = 120 pounds.

To find:

The weight of Marry in kilograms.

Solution:

We have,

2.2 pounds = 1 kilogram

Using this conversion, we get

1 pound = [tex]\dfrac{1}{2.2}[/tex] kilogram

120 pound = [tex]\dfrac{1}{2.2}\times 120[/tex] kilogram

                  = [tex]\dfrac{120}{2.2}[/tex] kilogram

                  [tex]\approx 54.54[/tex] kilogram

Therefore, the weight of Mary is about 54.54 kilograms.

What is the answer to this question

Answers

your answer would be C
if triangle efg is equal to hjk then it will still be equal the opposite way. The symmetric property tells us that both sides of the equal sign are equal no matter what side they are on.

Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.

Answers

Remember PEMDAS, you have to simplify the exponent first.

Find the total number of outcomes in each experiment. Write your answers on a sheet of paper.

1. tossing a coin
2. tossing 3 coins
3. rolling a die 10 times
4. rolling two dices
5. pressing a number key on a calculator
6. picking a card from a regular deck of cards
7. choosing a letter from the English alphabet
8. choosing a letter from the word OUTCOME
9. choosing a letter from the word PREDICTION
10. picking a crayon from a box with 36 crayons of different colors

Answers

Answer:

Step-by-step explanation:

In each option you need to find the number of outcomes of a single event and then multiply that by the number of times that event takes place.

1. 2 outcomes (heads and tails)

2. 6 outcomes (2 outcomes * 3 tosses)

3. 60 outcomes (6 outcomes per die * 10 rolls)

4. 12 outcomes (6 outcomes per die * 2 rolls)

5. 10 outcomes (10 numbers on the pad)

6. 52 outcomes (52 cards in a regular deck)

7. 32 outcomes (32 letters in the alphabet)

8. 7 outcomes (7 letters to choose from)

9. 10 outcomes (10 letters to choose from)

10. 36 outcomes (36 crayons to choose from)

Help me if you dont mind

Answers

Answer:

B

left side results in 42 and right side results in 42

How can I solve this problem

Answers

Answer:

x = 27

Step-by-step explanation:

I'm going to use letters to label the parts of the triangle while explaining how to solve for x:

Angle A = x (bottom left angle of the triangle)

Angle B = 4x (top angle of the triangle)

Angle C = empty angle (bottom right angle of the triangle)

Angle D = 3x + 54 (angle outside of the triangle)

A line has a angle measurement of 180 degrees.

Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.

To find Angle C, we would subtract Angle D's equation from 180 like this:

180 - (3x + 54)

Now Angle C equals 180 - (3x + 54)

Now we have all the angles inside the triangle. To find x, we are going to sum up  Angle A, B, & C and set it equal to 180.

We set the equation to 180 because a the sum of the interior angles for a triangle is 180.

The equation looks like this:

(180 - (3x + 54)) + 4x + x = 180

Now we use basic algebra to solve it:

(180 - (3x + 54)) + 4x + x = 180

(distribute the - to (3x + 54))

180 - 3x - 54 + 4x + x = 180

(add like terms on the left side of the equation)

126 + 2x = 180

(subtract 126 from both sides)

2x = 54

(divide both sides by 2)

x = 27

To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.

Hope it helps (●'◡'●)

Consider the following proportion:
2 12
— -—
7 x
Use cross products to write the equation: 2x = 84.
What is the value of x?

Answers

2x = 84 so 2x /2 = 84/= x=42

[tex]\displaystyle\bf 2x=84\\\\x=84:2=42\\\\\boxed{x=42}[/tex]

What is the measure of arc BC?
А
o
50°
25
E
C
D
pls help if u can:)

Answers

Answer:

arc BC = 100°

Step-by-step explanation:

The inscribed angle BEC is half the measure of its intercepted arc BC , then

arc BC = 2 × 50° = 100°

evaluate f(x)=1/4x for x=-5
option 1. -1/20
option 2. -1 1/4
option 3. 20
option 4. -4/5

Answers

Answer:

option 2. -1 1/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

FunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 1/4x

Step 2: Evaluate

Substitute in x [Function f(x)]:                                                                           f(-5) = 1/4(-5)Multiply:                                                                                                             f(-5) = -5/4Simplify:                                                                                                             f(-5) = -1 1/4

Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of seconds Lola needs to sign all 96 invitations?

508 seconds
510 seconds
509 seconds
508.8 seconds

Answers

Answer:

508.8 seconds

Step-by-step explanation:

The most accurate determination mathematically is to assume that Lola will maintain an average of 5.3 seconds per signature as she signs all 96 invitations.

Therefore, multiply the time it takes her to sign each invitation (5.3 seconds) by the total number of invitations there are (96 invitations) to get the projected total amount of time that it will take Lola to sign all 96 invitations:[tex]96\cdot 5.3=\boxed{508.8\text{ seconds}}[/tex]

Answer:

508.8 seconds (8.48 minutes)

Step-by-step explanation:

96 × 5.3 = 508.8

Can someone help me with this​

Answers

Answer:

Step-by-step explanation:

Paul rolls a fair dice 132 times.
How many times would Paul expect to roll a three?

Answers

There are 6 numbers on the dice, rolling a 3 would be 1/6

Multiply total rolls by probability of getting a 3:

132 x 1/6 = 132/6 = 22

The answer: 22 times.

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