Question

Create a quadratic equation in standard form that can be factored.

Part A. Write your equation in standard form. Use complete sentences to explain the benefits of writing your equation in standard form.

Part B. Write your equation in factored form. Use complete sentences to explain the benefits of writing your equation in factored form.

Part C. Write your equation in vertex form. Use complete sentences to explain the benefits of writing your equation in vertex form.

Answer 1

Part D. Explain how all three forms can be used together to help you graph a quadratic function. Graph your function, and label the y-intercept, the x-intercepts, and the vertex.

Answer 2

@triciaal @mathmale @mathstudent55 @zepdrix @sleepyjess @ganeshie8 @boldjon @pooja195 @ParthKohli @dan815 @nnesha

Answer 3

@Michele_Laino @imqwerty @robtobey @.Sam. @welshfella @jagr2713 @ikram002p @inkyvoyd @ShadowLegendX @rvc @Awolflover1

Answer 4

Can someone please help with this?

Answer 5

First, make an equation that you can factorize

Answer 6

Standard form is ax + by = c, correct?

Answer 7

Create a quadratic equation in standard form that can be factored.

Part A. Write your equation in standard form. Use complete sentences to explain the benefits of writing your equation in standard form.

First, what does a quadratic equation in standard form looks like?

Answer 8

@nincompoop A quadratic equation is a 2nd degree equation, right?

Answer 9

yes

Answer 10

yep

Answer 11

The Standard form of a quadratic equation is ax^2 + bx + c

I'm assuming they want a quadratic in ax + by = c form, correct?

Answer 12

the first one

Answer 13

yep

Answer 14

Oh, ax^2 + bx + c?

alright

Answer 15

EQUATION so do not forget the right side of the equation.

Answer 16

what you had was an EXPRESSION and not an equation.

Answer 17

12x^2 + 4x + 8 = 0?

Answer 18

something like that

Answer 19

"something like that" meaning something is wrong with my equation?

Answer 20

is that factorable ?

Answer 21

well, 4 can definetely be factored out of it

Answer 22

go on and then?

Answer 23

4(3x^2 + x + 2) = 0

Answer 24

ermmm...

Answer 25

hmm

Answer 26

so how would you factor the one inside the parenthesis in the left hand side?

Answer 27

what one?

Answer 28

(3x^2 + x + 2)

Answer 29

I'm getting really confused by your "one". Do you literally mean the number 1, or are you saying something else?

Answer 30

how do you factor the number 1? you cannot so it must be something else.

How do you factor "the one INSIDE the parenthesis" on the left hand side. DO you have anything that is enclosed in the parenthesis? YES (3x^2 + x + 2)

Now, factor it.

Answer 31

a common factor between 3x^2 and x is x, but what would happen with the 2?

Answer 32

I don't know. You tell me.

Answer 33

you are the one that came up with the equation, not me.

Answer 34

Is it possible to leave out a number from the equation when factoring?

Answer 35

meaning?

Answer 36

as in, could I do

4((3x + 1)2) ?

Answer 37

Wait, sorry that's wrong

Answer 38

4(x(3x + 1)2)

Answer 39

Like, is that possible in factoring, or do I have to include the 2 as well?

Answer 40

No. First, what is the number two doing there? is that suppose to be an exponent or what?

Answer 41

4(3x^2 + x + 2) = 0

Answer 42

That's what the number 2 is doing there

I factored x out of 3x^2 + x, is that allowed or do I have to find a GCF for all 3 terms inside the parantheses

Answer 43

No. That is incorrect.

Answer 44

alright

Answer 45

What is this? 4(x(3x + 1)2)

Answer 46

So is there any way to factor 4(3x^2 + x + 2) = 0 anymore? Any technique that I don't know?

Answer 47

4 ( 3x^2 + x + 2) = 0

Answer 48

You tell me! you're supposed to have learned this already.

Answer 49

You've been doing factoring for the past 3 weeks.

Answer 50

4 ( 3x^2 + x + 2) = 0

GCF Between 3x^2 and x = x

4 ( x( 3x + 1 ) + 2) = 0

Answer 51

That was my way of thinking when I got

4(x(3x + 1)2)

Although i forgot the + sign before the 2

Answer 52

How about this. Start with something simpler.

Answer 53

change your equation to something you can actually factor properly.

Answer 54

Fine

@nincompoop In anycase, is 4(3x^2 + x + 2) fully factored?

Answer 55

Well that is the farthest that you can do. But that is not a good expression, because you can't really further factor whatever you have inside the parenthesis. Remember that you've been factoring quadratic equations to something like (x+a) (x+b)

Answer 56

Is there some technique to know if a quadratic equation/expression is factorable in the first place?

Answer 57

Or do I just have to guess and check?

Answer 58

YES. You reverse what you have been learning to factor.

Answer 59

using FOIL, correct?

Answer 60

If you can factor \((x^2+8x+16) \) into \((x+4 ) (x+4) \) which gives you \((x+4)^2 \) then you can do the same thing in reverse way.

Answer 61

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

First
Inner
Outer
Last

x * x = 8x^2.

2 * 4x = 8x.

2x * 3 = 6x.

2 + 3 = 6

8x^2 + 8x + 6x + 6

Answer 62

Simplify:

8x^2 + 14x + 6

Answer 63

Done

Answer 64

Write your equation in standard form. Use complete sentences to explain the benefits of writing your equation in standard form.

Answer 65

it is an equation, so do not fail to forget the right-hand-side of the equation.

Answer 66

So just to clarify, I just completed Part A correct? I'm confused. Does standard form mean ax + by = c

or does standard form mean ax^2 + bx + c?

Answer 67

8x^2 + 14x + 6 = 0

Answer 68

NO. This is the standard-form:
\(ax^2+bx +c = 0 \)

Answer 69

so what is ax + by = c?

Answer 70

8x^2 + 14x + 6 = 0 this is correct

Answer 71

alright

Answer 72

Write your equation in factored form. Use complete sentences to explain the benefits of writing your equation in factored form.

Answer 73

factored form:

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

Answer 74

I don't know who taught you that ax + by = c is a quadratic equation
First, your highest degree of polynomial is not two, it is one

Answer 75

What are the benefits of having an equation in factored form?

Answer 76

Oh I just looked it up

Answer 77

what is the benefits from what you can tell?

Answer 78

Oh nevermind, that's standard form for a linear equation, not quadraic

Answer 79

exactly.

Answer 80

It's neater, easier to find out what x equals?

thats all i can think of

Answer 81

so what is the benefits of writing quadratic equations in standard form?

Answer 82

easier to find out what x equals @nincompoop ?

Answer 83

how?

Answer 84

sorry

forgot the = 0 part again

(2x + 2)(4x + 3) = 0

Answer 85

that is something you can tell in factored form

Answer 86

(2x + 2) = 0

(4x + 3) = 0

Answer 87

It is not always easy to tell what the values of x are in \(ax^2+bx+c= 0 \)

Answer 88

Then you can easily solve for x.

Are there actually any benefits other than that for writing a quadratic equation/expression in factored form?

Answer 89

@nincompoop ?

Answer 90

okay, let us test your answer but with a different equation. I will use what you originally had put
12x^2 + 4x + 8 = 0

Tell me what are the values of x in that equation?

Answer 91

no idea

Answer 92

well first, you can't easily factor so you can't easily find your x values.
So you can easily tell that it is not a perfect square trinomial. Perfect square trinomials are binomials multiplied by itself and an example is a binomial \(x+5\) when multiplied by itself becomes \((x+5)^2 \rightarrow (x+5)(x+5)\)

Answer 93

To be honest, the only benefit I can think of is you can find the x-intercepts, or solutions, or x value, or whatever you want to call it easily if it is fully factored and the equation is equal to 0. Beyond that my mind is a blank

Answer 94

Maybe that is the only benefit o_O

Answer 95

Write your equation in vertex form. Use complete sentences to explain the benefits of writing your equation in vertex form.