Consider the quadratic function defined by:

f (x) = −3(x −1)(x + 6)
a. State the zeros of the function: ____________________
b. Express this function in standard form by expanding & simplifying.

Answers

Answer 1

Answer:

[tex]\implies x = 1 \quad or -6 \\\\\implies f(x) = -3x^2-15x + 18 [/tex]

Step-by-step explanation:

Given :-

A quadratic function is given to us. The function is -3(x-1)(x-6)

And we need to find out the zeroes of the quadratic function and we need to express it in Standard form. T

Function :-

[tex]\implies f(x)= -3(x-1)(x+6) [/tex]

So for finding the zeroes equate it with 0 .So that ,

[tex]\implies f(x)=0 \\\\\implies -3(x-1)(x+6)=0 \\\\\implies (x - 1 )(x+6) = 0 \\\\\implies x = 1 \quad or \quad -6 [/tex]

Therefore the zeroes are 1 and -6 .

Expressing in Standard form :-

The standard form of a quadratic equation is ,

[tex]\implies ax^2+bx + c = 0 [/tex]

And that of a quadratic function is ,

[tex]\implies f(x) = ax^2+bx + c [/tex]

Simplifying the equation :-

[tex]\implies f(x)= -3(x-1)(x+6)\\\\\implies f(x) = (-3x +3)(x+6) \\\\\implies f(x) = -3x(x+6)+3(x+6)\\\\\implies f(x) = -3x^2 -18x +3x + 18\\\\\implies f(x) = -3x^2-15x + 18 [/tex]

Hence the Standard form of the equation is -3x² - 15x + 18 .


Related Questions

plz give step by step explanation
Which is a solution to the equation?
3x + y = 2

a) 4
b) (-1,2)
c) (3-5)
d) (1,-1)​

Answers

The answer is d because when you put the numbers into the equation you get 2 3(1)+(-1) you get 2

help for 100 points please please

Answers

Answer:

Step-by-step explanation:

Take the percentages for both 1992 and 2000 and make the average. that is your answer


18


2 simplify far as possible

Answers

Answer:

2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{2x9}[/tex] - [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex] - [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]

The mean and median of the five Numbers are the same 4 6 x y 10

Answers

The value of x is 7 and value of y is 8

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given data set is {4, 6, x, y, 10}

The mean and the median are the same value.

The median is the middle value, which is x, and the mean is:

M = (4 + 6 + x + y + 10)/5

Then we have that:

(4 + 6 + x + y + 10)/5 = x

Now let's solve this:

(4 + 6 + x + y + 10) = 5x

20 + x + y = 5x

20 + y = 4x

And x and y are whole numbers. Then we can take x = 7 to get:

20 + y = 4*7

y = 28 - 20 = 8

Then we have x = 7 and y = 8.

Hence, the value of x is 7 and value of y is 8 in the data set 4 6 x y 10

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In a school of 600 students, there are seven times as many right-handed pupils as left-handed pupils. How many pupils are right-handed?

Answers

Answer:

About 516 students are right handed.

Step-by-step explanation:

Divide 600 by 7 to get 85.7143. Round up to 86. Multiply times 6.

Answer:

I'll setup the problem and leave you to solve it

Step-by-step explanation:

L = number of left-handed students

R = number of right-handed students

you have 2 equations

L + R = 600 (1)

R = 7 x L (2)

solve for L in equation 1

L = 600 - R

substitute L in equation 2

R = 7(600 -R)

multiplying and gathering like terms

8R= 4200

solve for R and you have your answer

What is the slope of the line? (30 points)

Answers

Answer:

Slope = -1 or (-1/1)

Step-by-step explanation:

slope = m

Point 1: (0, 2); Point 2: (2, 0)

           (x₁, y₁)                (x₂, y₂)

        y₂ - y₁       0 - 2        -2

m = ----------- = ---------- = ------- = -1 or (-1/1)

        x₂ - x₁       2 - 0        2

I hope this helps!

on a tryangle if side a is 9 and side c is 19 then what is side b?​

Answers

Answer:

5

Step-by-step explanation:

Hello! Hope everyones doing ok. could use your help here:

1. Draw 16 stairs. Put them equally into 2 sets. How many stairs are in each set? ___

2. Round each number to the nearest 10. Then subtract : 497 - 315 is about: ___

3. Abel drew some Triangles. his drawing had 21 Vertices. How many triangles did he draw? write a division equation to answer the question: ___

Answers

Answer:

180

Step-by-step explanation:

500 - 320

180

this is answer hope it helps

How many solutions does the system y 3x 4 and 6x 2y 8 have?

Answers

The system y = 3x + 4 and 6x - 2y = 8 has no solutions.

A system of equations is a set of equations with multiple variables. To determine the number of solutions for a system of equations, one can use the following methods: graphing, substitution, or elimination. In this case, we can use the elimination method by adding or subtracting the equations to eliminate one of the variables.

If we add the two equations, we get y = 3x + 4 + 6x - 2y = 8, which results in 3x + 4 = 8. This is an inconsistent equation and does not have any solutions. Therefore, the system y = 3x + 4 and 6x - 2y = 8 has no solutions.

This shows that the system is inconsistent, which means that there's no solution that satisfies both equations.

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Olving ytem of linear equation in two variable
1. 4x8y=24 2. 2xy=19 3. 3x2y=15
4x2y=12 x-y=11 x2y=10

Answers

The solution of this system of linear equations is x=3, y=-5.

To solve this system of linear equations, you can use various methods such as substitution, elimination, or matrices. Here is one way to solve using the substitution method:

From equation 2, we can find the value of x in terms of y: x = (11+y)/2Substitute this value of x into equations 1 and 3:

4((11+y)/2) + 8y = 24

3((11+y)/2) + 2y = 15

Solve for y in the first equation: 8y = 24 - 44 = -20

y = -5

Substitute this value of y back into equation 2 to find x:

x = (11 + (-5))/2

x = 3

Substitute the values of x and y back into the original equations to check if they are correct:

4(3) + 8(-5) = 24

3(3) + 2(-5) = 15

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The question is -

Solving a system of linear equations in two variables,

4x + 8y = 242x - y = 113x + 2y = 15

Write an inequality for the situation. A number m is less than or equal to negative two.

Answers

So If m is less than or equal to negative two there are two ways you could write that: -2>m but you need to put a line under the greater than sign to create the less that or equal to sign. If you flipped that then it would also be the same: m<-2 with a line under the less than sign. Could you please mark branliest, thank you!

PLEASE HELP 10 POINTS

Answers

Answer:

the answer would be 1.35

Step-by-step explanation:

Find the value of x. Round to
the nearest tenth.
10
IX
500
X = [?]
Enter the number that belongs in
the green box.
Enter

Answers

Answer:

x = 88.2

Step-by-step explanation:

Reference angle = 10°

Opposite = x

Adjacent = 500

Apply TOA:

Tan 10° = x/500

Multiply both sides by 500

500*Tan 10° = x

88.1634905 = x

x = 88.2 (nearest tenth)

Decompose one number to subtract 726-340

Answers

The subtraction of the given number would be = 386

What is subtraction?

Subtraction is defined as one of the major arithmetic operations that is used to remove a value from another given values.

The subtraction of the value 340 from 726 would be = 386.

That is; 726 - 340 = 386

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Toni invests money into an account which pays a fixed rate compound interest each year.
The total value, £V, of her investment after 't' years is given by the formula=1350 x 1.04t.
How much did Toney invest?
if u get this ur a genius

Answers

Answer: Toni invested in pounds= $1350

Step-by-step explanation:rate of compound interest=4%

Step-by-step explanation:

Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula:  

Given equation is in the form of

where P is the amount invested

'r' is the rate of interest

t is the time taken

P= 1350 is the initial amount invested

1+r= 1.04  (subtract 1 from both sides)

multiply it by 100 to get percentage

r= 4%

I just search it bc my brain dosent work any more

which number is greater than the number at point p

Answers

I need a picture!!!!

PLS HELP
what would be the equation for this one?

Answers

Answer:

x^2 + y^2 = 25

Step-by-step explanation:

The standard form of a circle equation is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center and r is the radius.

We can see that the center is (0, 0) by looking at the graph, and the radius is 5 because it is marked. Plugging these in we get:

x^2 + y^2 = 25

Ashley is training to run a
marathon. On Monday,
she runs 21 miles in 3
hours
COP=??

Answers

Answer:

7

Step-by-step explanation:

Answer:

what is a COP huhhh?????

please help me with this

Answers

Answer:

i can't see the file can u share it to me

What is the length of the longer side ?

Answers

Answer:

C.11

Step-by-step explanation:

a perimeter is the total length of all sides of a rectangle. so

rectangle has 4 sides and it says that the shorter side is 5 so 5+5 for the shorter side and it's 10

32-10=22

22÷2= 11

(basta yan lang alam ko, sorry kung mali.)

Need to catch up on school work :/
Suppose a city with a population of 400,000 has been growing at a rate of 3% per year if this rate continues find the population of the city in 24 years , (round to the nearest whole number as needed)

Answers

Answer: 813,118 people in the city after 24 years

400,000(1+.03)^24

factor 8x^2+ 30x - 4x + 15

Answers

Answer:

(2x+5)x(4x+3)

Step-by-step explanation:

have a nice day

Is log e and log same?

Answers

The log function with base 10 is called the “common logarithmic functions” and the log with base e is called the “natural logarithmic function”. The logarithmic function is defined by, if logab = x, then ax = b.

The log with a base "e" (log e) is the same thing as In

The natural logarithmic function log e  refers to its logarithmic function of the base of the constant e. For this equation to be equivalent in logarithm;

We can say that:

log e = ln

Logarithm may alternatively be defined as the exponent power to which a base must be raised in order to produce a given number.

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What is value of tan 90?

Answers

Answer:

Step-by-step explanation: infinity or undefined.

A small snowcone costs $0.75 at the local snowcone shack. Mrs. Eckelberry had the snowcone shack deliver small snowcones for some of her students. She spent $18.75 for the snowcones. The equation 0.75s = 18.75 could be used to determine how many snowcones were ordered. How many snowcones did Mrs. Eckelberry order? * 16 pointsss!

Answers

Answer:

25 snowcones

Step-by-step explanation:

0.75s = 18.75, where (s) is the number of students/snowcones ordered

Divide both sides by 0.75:

0.75s/0.75 = 18.75/0.75

s = 25

I need help ASAP. Last Assignment for this class.
The center of a Ferris wheel is 55 feet above the ground. The Ferris wheel completes one revolution every 40 seconds. The distance between the lowest and highest points of the Ferris wheel is 100 feet. A trigonometric function models the height of the seat that starts closest to the ground when the wheel begins moving.
(a) What is the period of the function?
(b) What is the amplitude of the function?
(c) What is the midline of the function?
(d) Sketch the first two periods of the graph of the function.
Plot and label the key points of the graph. Label each axis with an appropriate scale.

Answers

Answer:

a squared plus b squared equals c squared

Step-by-step explanation the answer either your in for a bumpy ride

4 time 3=12

Answer:

The answer is C

Step-by-step explanation:

Galeno wants to buy a video game at a store having a 20% off storewide sale. The regular price of the video game is $50. The sales tax on the video game is 5.75%. How much does Galeno pay for the video game?

Answers

Answer:

42.30

Step-by-step explanation:

An amusement park has a collection of scale models, with ratio 1:20, of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica at this park, rounded to the nearest whole number

Answers

The height in feet of its replica at this park, rounded to the nearest whole number is 14 feet.

What connection exists between height and separation?

Distance is the measurement of an object's horizontal distance from a specific location, whereas height is the measurement of an object's height in the vertical direction.

Since the heights of real buildings are 1:10 times higher than those of model buildings, this is evident. We also know that the actual height of the US Capitol is 289 feet, so we divide that figure by 20 to determine the model's height. That amounts to 14.45, rounding to 14. Thus, the duplicate is 14 feet, rounded up to the nearest whole number.

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Your grandmother has given you some money, and now you plan to save what she has given you along with a certain amount of money each week. After 17 weeks, you have $570, and after 29 weeks, you have $822. a) Find an equation (in slope-intercept form) of the amount of money saved after × weeks.

Answers

An equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

What is the slope intercept form?

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Given that, after 17 weeks, you have $570, and after 29 weeks, you have $822.

Here, (17, 570) and (29, 822)

Substitute (x₁, y₁)=(17, 570) and (x₂, y₂)=(29, 822) in m=(y₂-y₁)/(x₂-x₁)

= (822-570)/(29-17)

= 252/12

= 21

Substitute, m=21 and (x, y)=(17, 570) in y=mx+c, we get

570=21×17+c

570=357+c

c=213

Substitute, m=21 and c=213 in y=mx+c, we get

y=21x+213

Therefore, an equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

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Find the value of y for the given x equal to a value. y=-2x+7 when x=-2

A. y=3
B. y=-3
C. y=11
D. y=-11

Answers

Y=-2(-2)+7
Y=4+7
Y=11
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