How many Identities are there in algebra?
Name them.​

Answers

Answer 1

Answer:

the technical number depends on what you are including to be algebraic identities.

There are multiple forms of most identities (pos. / neg.   and multiple ways of writing the same identity)

generally, you can consider there to be 10

Step-by-step explanation:

algebraic identity: an equality that holds true for any variable values

standard identities:

square of binomial:

(a+b)² = a² +2ab + b²

(a - b)² = a² - 2ab + b²

difference of squares:

(a + b)(a - b) = a² - b²

----

product of two binomials:

(x + a)(x + b) = x² + (a + b)x + ab

square of trinomial:

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

(x - y - z)² = x² + y² + z² -2(xy + yz - zx)

cube of binomial:

(x + y)³ = x³ + y³ + 3xy (x + y)

(x - y)³ = x³ + y³ - 3xy (x - y)

(a - b)³ = a³ - 3a²b + 3ab² - b³

sum of cubes:

a³ + b³ = (a + b)(a² - ab + b²)

x³ + y³ = (x + y)(x² - xy + y²)

x³ + y³ = (x - y)(x² + xy + y²)

difference of cubes:

a³ - b³ = (a - b)(a² + ab + b²)

x³ - y³ = (x - y)³ + 3xy(x - y)

--

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

                              = 1/2 (x + y + z) [(x -y)² + (y - z)² + (z - x)²]

(a + b + c)³ = a³ + b³ + c³ + 3(a + b)(b + c)(c + a)

--

and

if x + y + z = 0, then x³ + y³ + z³ = 3xyz

hope this helps!!

(this took me a while to write; there are also a few complicated identities also that I've left out)

Answer 2

[tex]( {a + b})^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ {a + b + c}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ \\ {a + b}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ {a - b}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) \\ \\ {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca).[/tex]


Related Questions

a dog is moving at a constant speed of 8 m/s. what is the dog’s acceleration

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Acceleration_{dog} = 0[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.

And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0

Henceforth, Acceleration of dog is 0 as well.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer: Acceleration = 0 ✅

Step-by-step explanation:

Hii, let me help you out! (:

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 1

Acceleration means "change in speed (which is also known as velocity, V, in physics) per a specific amount of time.

Part 1 is Successfully completed!

                                             

Part 2Our Dog Problem

Now let's focus on finding the acceleration of the dog.

Like I said above, [tex]\sf Acceleration=change\;in\;speed\;per\;a\;specific\;amount\;of\;time[/tex]

Well, we are provided with the information that the dog's speed is constant. This means that it doesn't change. So the dog keeps on moving at a speed of 8 m/s. This means that its speed doesn't change, so the change in speed is 0. And this means that its acceleration is 0.

Voila! There's our answer, cheers! (:

___________________

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Consider a student loan of $12, 500 at a fixed APR rate of 9% for 25 years.
a. Calculate the monthly payment
b. Determine the total amount paid over the term of the loan
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Answers

The monthly payment is; $104.9; The total amount paid over the term of the loan is; $31470

How to calculate APR?

We are given;

Loan principal = $12,500

Interest rate = 12%

Number of payments per year = 12 payments per year.

Loan term = 25 years.

Formula for monthly payment is;

PMT = (p * APR/n)/[1 - (1 + APR/n)^(-nY)]

Where;

p is principal

APR is interest rate

n is number of payments per year

Y is loan term

Thus;

PMT = (12500 * 0.09/12)/[1 - (1 + 0.09/12)^(-12 * 25)]

PMT = 93.75/(1 - 0.106288)

PMT = $104.9

B) Total amount paid over the loan term is;

A = PMT * m * n

where;

m is number of months in a year,

n is number of years

A = 104.9 * 12 * 25

A = $31470

C) The principal as a percentage of the loan is;

P/A = 12500/31470

P/A = 39.72%

Percentage paid for interest is = 100% - 39.72% = 80.28%

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Find f(-4) for f(x)=9(3)^x

Answers

Answer:

[tex] f(-4) = \dfrac{1}{9} [/tex]

Step-by-step explanation:

[tex] f(x) = 9(3)^x [/tex]

[tex] f(-4) = 9(3)^{-4} [/tex]

[tex] f(-4) = 3^2 \cdot 3^{-4} [/tex]

[tex] f(-4) = 3^{-2} [/tex]

[tex] f(-4) = \dfrac{1}{9} [/tex]

Answer:

1/9

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How much is Bob's net salary for the week? Question 32

Answers

Answer:

A. $152.00

Step-by-step explanation:

I'm 99% sure the net salary is just the 220 (gross salary) minus everything else taken away which is (42 + 7 + 15 + 4) = 68. 220 - 68 = 152 so Bob's net salary would be 152

(X+p)(x+q) what part of the trinomial will equal the product of p and q?

Answers

The part of the trinomial that will equal the product of p and q is the constant part

How to determine the part?

The expression is given as:

(x + p)(x + q)

From the expression, p and q are both constants.

When a constant is multiplied to another, the result is a constant

This means that:

pq = constant

Hence, the part of the trinomial that will equal the product of p and q is the constant part

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the probability that Luis will pass his test is 0.82. find the probability that he will fail his statistic test

Answers

The probability of failure for Luis will be 0.18.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability of passing is = 0.82

We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-

Probability of failing = 1 - probability of passing

Probability of failing = 1 - 0.82

Probability of failing = 0.18

Therefore the probability of failure for Luis will be 0.18.

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1.) I can find my Vulome if the vulome of cylinder is multiplied by 4/3 who am i?
2.)The Vulome is 1/3 that of a cylinder that has the same base and height with me. Who am I?

Answers

If the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Thus, you're a sphere.

How to calculate the volume of a cone?

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

h is the height.r is the radius.

How to calculate the volume of a sphere?

Mathematically, the volume of a sphere can be calculated by using this formula:

V = 4/3 × πr³

Similarly, the volume of a cylinder can be calculated by using this formula:

V = πr²h

In this context, we can infer and logically deduce that if the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Also, multiplying the volume of a cylinder by 1/3 would produce the volume of a sphere.

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please answer me please​

Answers

Step-by-step explanation:

please mark me as brainlest

Answer: (2x + 5)(2x + 5)

Step-by-Step Explanation:

Factorize by Splitting the Middle Term :-

4x^2 + 20x + 25
4x^2 + 10x + 10x + 25
2x(2x + 5) + 5(2x + 5)
(2x + 5)(2x + 5)

This is the Factorized Form.

Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line
7x + 4y
10. Use exact values.

Answers

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

Answer:  [tex]\textsf{y = -1.75x - 11.75}[/tex]

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

Given:  [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution: We need to first solve for y in the equation that was provided so we can determine the slope.  Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.

Subtract 7x from both sides

[tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex][tex]\textsf{4y = 10 - 7x}[/tex]

Divide both sides by 4

[tex]\textsf{4y/4 = (10 - 7x)/4}[/tex][tex]\textsf{y = (10 - 7x)/4}[/tex][tex]\textsf{y = 10/4 - 7x/4}[/tex][tex]\textsf{y = 2.5 - 1.75x}[/tex]

Plug in the values

[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]

Simplify and distribute

[tex]\textsf{y + 3 = -1.75(x + 5)}[/tex][tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex][tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]

Subtract 3 from both sides

[tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 11.75}[/tex]

Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75

Four students were asked to write an expression which has terms that have a greatest common factor of ab. The
expressions provided by the students are shown below.
Olivia
20ab-14abc
Michelle
16a+3b
Michelle
Naomi
Which student wrote the correct expression?
O Olivia
O Peyton
Naomi
18abc-13abc
Peyton
15abc+ 14ab

Answers

Answer: Peyton

Step-by-step explanation:

Michelle: Greatest common factor is 1

Naomi: Greatest common factor is abc

Olivia: Greatest common factor is 2ab

Peyton: Greatest common factor is ab

Preston is correct -

g(x)=f(x)-3 which statement best describes the graph of g(x) with the graph of f(x)

Answers

Answer: The graph of g(x) is the graph of f(x) shifted 3 units down.

If f(x)=5x-2 and g(x)=2x1 find (f+g)(x)

Answers

Answer:

D

Step-by-step explanation:

5x-2+2x+1

5x+2x+1-2

7x-1

se the distributive property to remove the parentheses.
-(-3v-4w+1)

Answers

Hii!

[tex]\leadsto\parallel\boldsymbol{Answer.}\parallel\gets[/tex]

_________________________________________________________

3v+4w-1

__________________________________________________________

[tex]\leadsto\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]

We use the distributive property to "distribute" the minus sign.

[tex]\sf -(-3v-4w+1)=-1\cdot(-3v)+(-1)\cdot(-4w)+(-1)\cdot1}[/tex].

Simplify!

[tex]\sf 3v+4w-1}[/tex]. Which is our final answer.

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]

[tex]\boldsymbol{-Greetings!-}[/tex]

_________________________________________________________

Expand each expression A ( x+1)^2 B(x-3)^2. C ( x+4)^2 D (x-1/2)^2

Answers

The expanded expressions are shown below:

(x + 1)² = x² + 2 · x + 1(x - 3)² = x² - 6 · x + 9(x + 4)² = x² + 8 · x + 16(x - 1/2)² = x² - x + 1/43 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75(1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2

How to expand perfect square trinomials

Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:

a) (x + 1)² = x² + 2 · x + 1

b) (x - 3)² = x² - 6 · x + 9

c) (x + 4)² = x² + 8 · x + 16

d) (x - 1/2)² = x² - x + 1/4

e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75

f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2

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Immediate help needed please.
Can you answer and explain please

Answers

The possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

What is a quadratic equation?

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

(k - 1)x² + (4k)x + k -3 = 0

Here,

a = k - 1

b = 4k

c = k - 3

As we know for distinct real roots:

D > 0

[tex]\rm {b^2-4ac}} > 0[/tex]

(4k)² - 4(k-1)(k-3) > 0

[tex]\rm 16k^2-4\left(k-1\right)\left(k-3\right) > 0[/tex]

[tex]\rm 12k^2+16k-12 > 0[/tex]

[tex]\rm 3k^2+4k-3 > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2-\dfrac{13}{3} > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{3}[/tex]

[tex]\rm \left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{9}[/tex]

[tex]\rm k < \dfrac{-\sqrt{13}-2}{3}\quad \mathrm{or}\quad \:k > \dfrac{\sqrt{13}-2}{3}[/tex]

or

[tex]\rm k < -1.868 \quad \mathrm{or}\quad \:k > 0.535[/tex]

Thus, the possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

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if the relationships below are given in the form(input, output) which paring always describes a function

Answers

The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.

What is a Function ?

A function is a law that relates a dependent and an independent variable.

The options mentioned below needs to be studied to determine which forms a function.

Option A , C and D doesn't really form a function ,

For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.

height of a building in feet, height of the building in inches

Height of building in feet = (height of building in inches/12)

so this is a function

Therefore Option B is the right answer.

The missing options are

If the relationships below are given in the form (input, output), which pairing always describes a function?

A) (number of doors in a car, number of cup holders in the car)

B) (height of a building in feet, height of the building in inches)

C) (beverage charge on a bill, total meal charge on the bill)

D) (distance from home during a trip, time elapsed during the trip)

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In your own words, explain the discriminant test. Use the discriminant test to decide whether the equation represents a parabola, ellipse or a hyperbola and explain why you know this is true. x^2 − 4xy + 3x + 25y − 6 = 0

Answers

A discriminant test is one that tells whether a formula has one, two or no solutions.

The equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.

What is a discriminant test?

A discriminant test is a test that tells whether there are one, two or no solutions for a formula.

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.

The discriminant of a quadratic equation is given as ax2 + bx + c = 0

A discriminant is said to be a parabola either x or y is squared and not both unlike that of an eclipse and a hyperbola.

With the given equation,  x^2 − 4xy + 3x + 25y − 6 = 0, only x is squared and not both x and y.

Thus, the equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.

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3+7=6-|-x|
Solve for x.
Thanks :)

Answers

Answer:

no solution

Step-by-step explanation:

| | is a notation for absolute value, which is the distance that a number is from 0.

you can think of this as the "positive version" of a number

so, |-x| will become: x

We can plug this into the equation, and solve like we would for any variable

3 + 7 = 6 - |-x|  {simplify}

3 + 7 = 6 - x   {simplify}

10 = 6 - x

Now, we can isolate x (isolate = get it alone)

10 = 6 - x

-6     - 6    {subtract 6 from both sides}

 4 = -x         {multiply both sides by -1 to get positive x}

·-1   ·-1

- 4 = x

{check solution:}

3 + 7 = 6 - | -4 |

10 = 6 - 4

10 = 2

FALSE

because this solution has been found to be false, there is no possible value for x

we write this as: no solution

[tex]3+7=6-|-x|\\10=6-|x|\\|x|=-4\\x\in\emptyset[/tex]

Mitch needs to do his laundry. It takes him 75 minutes to do each load
when he washes and dries the load. It takes him 43 less minutes if he
hangs up his laundry to dry. He decides to hang up one load of laundry
to dry.
Mitch writes the equation 75r -43 = 332, where x is the number of loads
of laundry he needs to do in order to determine how long it is going to
take him.
The next step Mitch wrote to solve the equation is shown here: 75r = 375
Which property did he use to get to this step?
A
addition property of equality
B
distributive property
C
subtraction property of equality
D
combining like-terms

Answers

Answer: [A] addition property of equality

Step-by-step explanation:

    Mitch used the addition property of equality because he added 43 to both sides of the equation.

         75r - 43 = 332

         43 + (75r - 43) = (332) + 43

         75r = 375

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Which equation has a constant of proportionality equal to 1/2

Choose 1 answer:

Answers

For equations that model direct variation, they are of the form y = kx, where k is the constant of proportionality.

So, for there to be a constant of proportionality of 1/2, the equation should be y = 1/2 x.

This is the same as y = 3/6 x (since 1/2 = 3/6), so the answer is C.

Which of the following best describes a tessellation?
O A. An arrangement of repeating shapes with spaces between the
shapes and overlapping shapes
B. The point about which an image is rotated in rotational symmetry
C. An arrangement of repeating shapes with no spaces or overlaps
between them
D. The axis about which an image is rotated in reflectional symmetry

Answers

The statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C

What is tessellation?

A tessellation can be defined as a pattern of geometric shapes that fill a two-dimensional space without gaps and overlaps

It is also known to repeat infinitely in all directions.

Thus, the statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C

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Fill in the blank. In the triangle below, y=? Round your answer to two decimal places.

Answers

Answer:

z= 38°

Step-by-step explanation:

z= 90(from right angle)+52=142

180-142=38°

Britney sells mattresses at a furniture store. She makes a 9.75% commission on each mattress she sells. Last week, Britney sold four mattresses. The sale price of each mattress is shown in the table.

How much did Britney earn last week?

Enter your answer in the box.

$

Mattress sale Amount
Mattress 1 $2400
Mattress 2 $3200
Mattress 3 $1900
Mattress 4 $800

Answers

Answer:

$809.25

Step-by-step explanation:

→ Find the sum of the sales amount

2400 + 3200 + 1900 + 800 = 8300

→ Find the amount that s commission

( 9.75 × 8300 ) ÷ 100 = $809.25

A student survey his classmates to determine their favorite movies

Answers

Answer:

The answer is C. Hope it helps

file attached belowfile attached below

Answers

answer: theres nothing there buddy

explanation: im not sure what youre asking

The Candle Factory is producing a new candle. It has a radius of 3 inches and a height of 5 inches. How much wax is needed to make the candle? Use 3.14 for Pi. Round to the nearest whole cubic inch.

A cylinder with a radius of 3 inches and height of 5 inches.

Recall the formulas S A = 2 pi r squared + 2 pi r h and V = pi r squared h.
141 cubic inches
236 cubic inches
443 cubic inches
565 cubic inches

Answers

Answer:

141 cubic inches

Step-by-step explanation:

The candle can be modeled as a cylinder.

To find how much wax is needed to make the candle, calculate the volume of the cylinder.

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

r = 3 inh = 5 inπ = 3.14

Substitute the given values into the formula and solve for V:

[tex]\implies \sf V=3.14 \cdot 3^2 \cdot 5[/tex]

[tex]\implies \sf V=3.14 \cdot 9 \cdot 5[/tex]

[tex]\implies \sf V=28.26 \cdot 5[/tex]

[tex]\implies \sf V=141.3\:in^3[/tex]

Therefore, the amount of wax needed to make the candle is 141 cubic inches (nearest whole cubic inch).

please help me i am struggling

Answers

The Equation is represented as  [tex]\rm F = \dfrac{9}{5} (K -273.15 ) +32[/tex]

Option B is the answer.

What is an Equation ?

An equation is am mathematical statement formed when an algebraic expression is equated by an equal sign with another algebraic expression or a constant.

A Equation is given in the question

[tex]\rm K = \dfrac{5}{9}(F -32) +273.15[/tex]

where K denotes temperature in Kelvins and F denotes Fahrenheit .

To convert the equation in terms of K it can be rewritten as follows

[tex]\rm K = \dfrac{5}{9}(F -32) +273.15\\\\K -273.15 = \dfrac{5}{9}(F -32) \\\\\dfrac{9}{5} (K -273.15 ) = F - 32\\\\F = \dfrac{9}{5} (K -273.15 ) +32[/tex]

Therefore Option B is the right answer.

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Please solve these questions with an explanation

Answers

Answer:

Step-by-step explanation:

2 ft
4.5 ft
6 ft
A) 38 cubic feet
B) 54 cubic feet
C)
66 cubic feet
D) 125 cubic feet
What is the volume?

Answers

Answer:

B

Step-by-step explanation:We know Volume = (a*b*c)

Answer:

B) 54 cubic feet

Step-by-step explanation:

DRaw the graph of f (x) = 1/2 x² -2x where -2 < x < 4​

Answers

Answer:

Graphs Attached Below

Step-by-step explanation:

Hello!

Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]

From our Equation:

a = 1/2b = -2c = 0

There are several values that are needed to drawing a parabola:

y - interceptAxis of Symmetry (AOS)Vertexx - intercepts

Y-intercept

Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]

The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.

Axis of Symmetry

A parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.

To calculate the AOS, we use the formula [tex]AOS = \frac{-b}{2a}[/tex], from the values of the equation.

Calculate

[tex]AOS = \frac{-b}{2a}[/tex][tex]AOS = \frac{-(-2)}{2(0.5)}[/tex][tex]AOS = \frac{2}{1}[/tex][tex]AOS = 2[/tex]

The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.

Vertex

The vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.

To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.

Calculate

[tex]f(x) = \frac12x^2 - 2x[/tex][tex]f(x) = \frac12 (2)^2 - 2(2)[/tex][tex]f(x) = 2 - 4[/tex][tex]f(x) = -2[/tex]

The y-value is -2. The vertex is (2, -2).

X-intercepts

The x-intercepts are the points where the graph intersects the x-axis (y = 0).

Solve by Factoring

[tex]f(x) = \frac12 x^2 - 2x[/tex][tex]0 = \frac12x(x - 4)[/tex][tex]x = 0, x = 4[/tex]

The roots are (0,0) and (4,0).

Graph

Now we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.

Image Attached

Domain Restrictions

The Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.

That means we remove the parts of the line that don't belong in that domain.

Image Attached

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