explain the benefits of each of the three forms of quadratic equations, standard form, vertex form, and factored form. What do they reveal about the graph or the quadratic?

Answers

Answer 1

Answer:

Summary:

Standard form allow us to quickly find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Step-by-step explanation:

The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.

Standard Form:

The standard form of a quadratic is:

[tex]ax^2+bx+c[/tex]

There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.

The leading coefficient a will tell us if the parabola curves upwards or downwards.

And the constant c will give us the y-intercept.

Vertex Form:

The vertex form of a quadratic is:

[tex]a(x-h)^2+k[/tex]

There are also two details that can be conveyed by a quadratic in vertex form:  (1) the vertex, and (2) the leading coefficient.

The leading coefficient is given by a. Again, this tells us the orientation of the parabola.

And the vertex is given by (h, k).

Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.

Factored Form:

The factored form of a quadratic is:

[tex]a(x-p)(x-q)[/tex]

Where p and q are the zeros/roots/solutions of the quadratic.

Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.

The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.

Summary:

Therefore, each form of a quadratic equation has its own benefits.

Standard form allow us to find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Hence, depending on the question, each form can be useful in its own way.


Related Questions

whats -9+2345+5678+4567

Answers

Answer:

I got 12581

Step-by-step explanation:

Tyler swims at a constant speed, 6 meters every 4 seconds. How long does it take him to swim 114 meters?

Answers

Answer:

91.2 seconds

:)

Answer:

76 seconds (1:16 one hour and 16 minutes)

Step-by-step explanation:

You take the distance that he has to travel (114m) and you divide it by the distance you're given that he is moving at every time (6m). this gives us 19. Then you take that and multiply it by how many seconds it takes him to move the given 6m (4s), which gives us an answer of 76 seconds


A line passes through point (8, -2) and has a slope of -5/4
Write an equation in Ax+By= C form for this line.
Use integers for A, B, and C.
show work on how you got it

Answers

Answer:

4y+5x=32

Use slope intercept form, then change to Ax+By= C form.

slope word problems for slope

Answers

Answer:

number 10 (5/6)

Step-by-step explanation:

hope this helped ^^

At the end of the harvest season, Omar wonders if it is time to cover the garden with a tarp. He understands that as the temperature decreases, moisture in the air condenses into dew which freezes at 0 degrees Celsius and may damage the plants in the garden.

Answers

Answer:

no clue im stuck on it to

Step-by-step explanation:

Answer:

No Omar does not have to put the blanket

Step-by-step explanation:

The answer is No ,because since Omar only covers the plant when its below 0 , And when  the temperature is 5 degrees Celsius at 4:00 pm  and the  temperature is predicted to decrease 0.5 degrees Celsius every two hours until 4:00 am.  So 6 times 0.5 =3  so 5 - 3 = 2

Show work

4:00 pm     Fact :  And  very two hrs 0.5 degrees .

5:00 pm 1

6:00 pm 2 = 0.5

7:00 pm 1

8:00 pm  2 = 0.5

9:00 pm 1

10:00 pm 2 =0.5

11:00 pm 1

12:00 pm 2 =0.5

1 :00 Am 1

2: 00 Am 2 =0.5

3:00 Am 1

4:00 Am  2= 0.5

If jim had 8 apples and you took 5 away and gave him two back how many apples do you have?

Answers

5 apples is the correct answer:)

points (2, 5) and (-1, -4) and determine the equation of the line.

Answers

Find slope: (y2-y1)/(x2-x1)
(-4-5)/(-1-2) = -9/-3 = 3
Y = 3x + b
5 = 3(2) + b, b = -1
Equation: y = 3x - 1

Solve the following system of equations.
6x + y = -3
6x + 5y = 9
please helpp

Answers

Answer:

x=3

y=-1

Step-by-step explanation:

Rate me brainliest pls


What’s the value for y?

Answers

Y=3(2)-2
Y=6-2
Y=4
The value of y is 4.
i agree with sujeidi

O triplo de um número inteiro X, pode ser representado por?

Answers

Answer:

hola

Step-by-step explanation:

which would be an appropriate first step in solving the equation? 2(x+3)-5=9

Answers

Answer:

Distributing

Step-by-step explanation:

Order of opersations says to do parenthesis first so....

2(x+3)-5=9

we would distribute 2

2x+6-5=9

Answer: x=4

and wydm

What are the solutions to this quadratic equation?

-2x^2+x+4=0

Answers

Answer:

Well I got [tex]\frac{1}{4} plus or minus \sqrt{33}[/tex]

Step-by-step explanation:

1/4±[tex]\sqrt{33}[/tex]

Answer:

The person above is correct this is just confirmation

Step-by-step explanation:

consider the function f(x) =4x-5. What is the domain value that correspons to an output of f(x) = 11

Answers

Answer:4 replace f(x) with 11 a

what is 2710 divided by 759?

Answers

It’s 3.570 most teachers would probably just want 3.5

Answer:

3.57048748 or (rounded) 3.57 or 3.5

Step-by-step explanation:

2710 ÷ 759 = ?

   2710

÷   759

3.57048748

(Rounded) = 3.57 or 3.5

Hopefully this helps! Sorry if wrong. You are loved and you are beautiful/handsome!

-Bee

Someone please help me with this chart, I don’t understand it.

Answers

Answer:

The second one is (3 x 3 x 3 x 3) x (3 x 3)

Step-by-step explanation:

write 2 differnt inequalities that can be solved by adding 2 to each side and dividing each side by -12

Quick!!

Answers

Answer:

-12x - 2 < -62

-12x - 2 > 34

Step-by-step explanation:

1. Start with

x > 5

Multiply both sides by -12.

-12x < -60

Subtract 2 from both sides.

-12x - 2 < -62

2. Start with

x < -3

Multiply both sides by -12.

-12x > 36

Subtract 2 from both sides.

-12x - 2 > 34

Answer:

-12x - 2 < -62

-12x - 2 > 34

how do I compare y intercepts and rates of change.​

Answers

Rates of change is the slope in Wich a line moves across the graph in a linear line. A y intercept is the vertical intercept in Wich the line is identified depending on if it is linear.

Write a slope-intercept equation of the line that passes through the points (4,11) and (6,8).



IN ADDITION TO THE EQUATION, YOU MUST IDENTIFY THE SLOPE AND Y-INTERCEPT OF YOUR EQUATION TO GET FULL CREDIT.

Answers

Answer:

y=[tex]\frac{3}{-2}[/tex]x +17

Step-by-step explanation:

[tex]\frac{11-8}{4-6}[/tex]=[tex]\frac{3}{-2}[/tex]=slope

11=[tex]\frac{3}{-2}[/tex] *4 + C

11=-6 + C

17=C=Y-intercept

In isosceles triangle ABC the segment BD is the median to base line AC. Find BD if the perimeter of the triangle is 50m and the perimeter of ABD is 40 m

Answers

Answer:

BD = 15 m

Step-by-step explanation:

Mathematically, we can find the perimeter of a triangle by adding all of the sides

Mathematically, the line from the top vertix of an isosceles triangle is perpendicular to the base line

So what this mean is that it splits the base line into 2 equal parts

So, in this case, since AC is base;

AD = CD

Please check the attachment for diagrammatic representation

So from the diagram;

25-x + x + BD = 40

25 + BD = 40

BD = 40-25

BD = 15 m

Suzie scored 75% on her assignment. If she got 15 questions correct, how many total questions were on the assignment?

Answers

Answer:

20 Questions Total

Step-by-step explanation:

15 divided by 20 = .75 = 75%

Answer:

2

Step-by-step explanation:

What is the equation of the line that passes through the point (-6,6) and has an undefined slope ?

Answers

Answer:

x = -6

Step-by-step explanation:

Ill give brainlist.

Answers

Answer:

True

Step-by-step explanation:

(0,-1) lands on the y-axis

Answer:

the answer is false

Step-by-step explanation:

bc the line is not on 0,-1

hope this helped ^^

select the correct answer​

Answers

Answer:

c

Step-by-step explanation:

What is 111/6 and 4 1/3 as an improper fractions?​

Answers

Answer:

Step-by-step explanation:

111/6 = 37/2

4 1/3 = 13/3

What is the answer to 2x^2+9x-35

Answers

Answer:

There is a graph of the algebraic equation as well as the simplified form of the problem, hope this helps.

Step-by-step explanation:

May I have brainliest please? :)

7 times 10 to the -7 power

Answers

Answer:

0.0000007 as a regular notation

or 7x10^-7 as scientific notation

1. A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85% (a) Write an equation to represent this situation. (b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%?​

Answers

Answer:

She would need to make 5 consecutive free successful throws

Step-by-step explanation:

Equations

A basketball player wants to improve his percent of successful throws to 85%.

She currently has made 12 out of 15 free throws, which gives a success percentage of 12/15*100=80%

So, she needs a number of free consecutive free throws to increase that number to the desired target.

The percentage of success can be calculated as:

[tex]\displaystyle P=\frac{\text{successful throws}}{\text{total throws}}*100[/tex]

Let's assume x is the number of required consecutive successful throws. Since she has already thrown 15 times, out of which has had 12 successful throws, now she will have 15+x total throws and 12+x successes, thus the new percentage is:

[tex]\displaystyle P=\frac{12+x}{15+x}*100[/tex]

And this percentage must be equal to 85%, thus:

[tex]\displaystyle \frac{12+x}{15+x}*100=85[/tex]

a) The equation to represent the situation is:

[tex]\mathbf{\displaystyle \frac{12+x}{15+x}*100=85}[/tex]

b) Let's solve it.

Multiply by 15+x:

[tex]\displaystyle (12+x)*100=85(15+x)[/tex]

Dividing by 5:

[tex]\displaystyle (12+x)*20=17(15+x)[/tex]

Operating:

[tex]\displaystyle 240+20x=255+17x[/tex]

Subtracting 17x and 240:

[tex]\displaystyle 20x-17x=255-240[/tex]

Simplifying:

[tex]\displaystyle 3x=15[/tex]

Dividing by 3:

x = 5

She would need to make 5 consecutive free successful throws

The number of throws is an illustration of proportions.

The number of free throws to raise her percent to 85% is 5

(a) The equation

The proportion is given as: 12 out of 15.

Let the number of throws be n.

So, the proportion would be:

[tex]\mathbf{Proportion = \frac{12 + n}{15 + n}}[/tex]

To make 85% success, then the proportion must equal 85%.

So, we have:

[tex]\mathbf{\frac{12 + n}{15 + n} = 85\%}[/tex]

(b) The solution to the equation

In (a), we have:

[tex]\mathbf{\frac{12 + n}{15 + n} = 85\%}[/tex]

Express 85% as decimal

[tex]\mathbf{\frac{12 + n}{15 + n} = 0.85}[/tex]

Cross multiply

[tex]\mathbf{12 + n = 0.85(15 + n)}[/tex]

[tex]\mathbf{12 + n = 12.75 + 0.85n}[/tex]

Collect like terms

[tex]\mathbf{n -0.85n= 12.75 -12 }[/tex]

[tex]\mathbf{0.15n= 0.75}[/tex]

Divide both sides by 0.15

[tex]\mathbf{n= 5}[/tex]

Hence, the number of free throws to raise her percent to 85% is 5

Read more about proportions at:

https://brainly.com/question/21126582

hello can u help plz?

Answers

Answer:

slope would be 3 or 3/1

Step-by-step explanation:

I think i'm not totally sure it could be -3 or -3/1

I need to find out how many kilometers mikalea can run in 1 hour

Answers

Answer:

I think its 10km in 1 hour.

Step-by-step explanation:

mikaela is running 5mg in 0.5 hours, but your looking for an 1 hour so you double it.

Find the sum of QR
4x+33

Answers

Answer:

Step-by-step explanation:

Simplifying

4x + 5 = 33

Reorder the terms:

5 + 4x = 33

Solving

5 + 4x = 33

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.

5 + -5 + 4x = 33 + -5

Combine like terms: 5 + -5 = 0

0 + 4x = 33 + -5

4x = 33 + -5

Combine like terms: 33 + -5 = 28

4x = 28

Divide each side by '4'.

x = 7

Simplifying

x = 7

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