Question

Look at the quadratic equation below.

-x2 + 3 = (2x - 1)2

What is this quadratic equation written in standard form?

A. 5x2 - 4x - 2 = 0
B. 3x2 - 4x - 2 = 0
C. 3x2 - 4x + 4 = 0
D. 5x2 - 4x + 4 = 0

Answer 1

@pooja195 @jigglypuff314 @Michele_Laino @imqwerty @KendrickLamar2014 @rebeccaxhawaii

Answer 2

\(-x^2 + 3 = (2x - 1)^2 \)

step 1-
simplify the right hand side part

to do that use this identity-
\((a-b)^2=a^2+b^2-2ab\)


step2-
bring all the terms one one side

step 3-
combine like terms and simplify

Answer 3

can u do it with me

Answer 4

how do i simplfiy the right side

Answer 5

yeah
:0

Answer 6

* :)

Answer 7

how do i do \((a-b)^2=a^2+b^2-2ab\)

Answer 8

okay we go like this-

we use this identity-
\((a-b)^2=a^2+b^2-2ab\)

now we look at our equation-
\(-x^2 + 3 =\color{red}{ (2x - 1)^2}\)

simplifying-
\(-x^2+3=(2x)^2 +(1)^2 -2(2x)(1)\)

Answer 9

confused ): that stuff looks really complicated

Answer 10

its okay :)
did you get that part where we used the identity?

Answer 11

no i did not ):

Answer 12

what is with the colors?

Answer 13

maybe if u drew it i would understand? because u dont get that );

Answer 14

i just used the colors to co relate that bracket thing with the identity

Answer 15

is there another way of doing this? or another way to show me

Answer 16

okay
what we did was-
\(-x^2 + 3 =\color{red}{ (\color{blue}{2x} - \color{green}1)^2}\)

we need to expand that bracket on the right
so we use this identity-> \((a-b)^2=a^2+b^2-2ab\)

look at the colored thing
\(\color{red}{(\color{blue}{2x} - \color{green}1)^2}\)

now use this identity-> \(\color{red}{(\color{blue}a-\color{green}b)^2}=a^2+b^2-2ab\)
\(\color{red}{(\color{blue}{2x} - \color{green}1)^2}=(2x)^2+(1)^2-2(2x)(1)\)

so our equation becomes-
\(-x^2 + 3 =\color{red}{ (\color{blue}{2x} - \color{green}1)^2}\)

\(-x^2 + 3 =(2x)^2+(1)^2-2(2x)(1)\)

Answer 17

maybe this could help-
http://prntscr.com/amjf6m

Answer 18

prntscr is blocked on school internet

Answer 19

i looked it up on my phone can u explain the picture

Answer 20

3-x²=(2x-1)²

Answer 21

are you stuck on the 2nd step?

Answer 22

yes

Answer 23

are you familiar with this identity-> \((a-b)^2=a^2+b^2-2ab\)

Answer 24

no, i am fimilar with ax²+bx+c=0

Answer 25

well in this question we need to use that identity
so i suggest that you watch this video-> https://youtu.be/Gr1E7TtXQ9U

it will help you clear that 2nd step

Answer 26

youtube is blocked on school internet

Answer 27

well then check out the 2nd identity given here- http://www.ask-math.com/factorization-using-identities.html

Answer 28

1) a2 + 2ab + b2 = (a + b)2

2) a2 – 2ab + b2 = (a – b)2

3) a2 – b2 = (a + b) (a – b)

4) x2 + (a + b) x + ab = (x + a) (x + b)