anonymous
  • anonymous
Find the x-intercepts of the parabola with vertex (-4,2)and y Intercept (0,-30) Wright answer if this form (x1,y1)(x2,y2).
Algebra
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i would also like to know how you did it
Nnesha
  • Nnesha
what's the vertex form of the parabola ?
anonymous
  • anonymous
(y-k)=a(x-h)^2

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anonymous
  • anonymous
Nnesha
  • Nnesha
hmm add k both sides so it would be \[\huge\rm y=a(x-h)^2+k\] vertex form where (h,k) is the vertex so substitute (h,k) for ( -4,2)
anonymous
  • anonymous
so like (y-2)=a(x--4)^2
Nnesha
  • Nnesha
ye that would work so y-intercept is (0,-30) where x =0 and y =-30 so plugin \[\huge\rm -30-2=a(0-(-4))^2\] now solve for a
anonymous
  • anonymous
so a =-2
anonymous
  • anonymous
i appreciate your help btw
Nnesha
  • Nnesha
yes right now u can find x-intercept \[\huge \rm -30-2=-2(x-(-4))^2\] solve for x let me know if you don't know how to work it out
anonymous
  • anonymous
x= 0,-8 Correct?
Nnesha
  • Nnesha
hmm plz show a little work...
anonymous
  • anonymous
im using an online calculator because the only calculator we have broke im not quite shure how to do the steps myself without it.
Nnesha
  • Nnesha
hmm well do you want to know how to work it out without calculator ?
anonymous
  • anonymous
couldent hurt mind if i get my notepad and pencil
anonymous
  • anonymous
ok i got it
Nnesha
  • Nnesha
alright first we can multiply negative by (-4) -1 times -4 = 4 ( negative times negative = positive ) \[\huge \rm -30-2=-2(x+4))^2\] -30-2 = -32 \[\huge \rm -32=-2(x+4)^2\] now we should foil (x+4)^2 `(x+4)^2 `is same as (x+4)(x+4)
Nnesha
  • Nnesha
|dw:1443017713689:dw| now we should distribute 2nd parentheses by first and 2nd term of the 2nd parentheses (foil method ) so multiply left first term by top
Nnesha
  • Nnesha
x(x+4) =??
anonymous
  • anonymous
x^2+4x ?
anonymous
  • anonymous
or dise tge 4 not have an x
Nnesha
  • Nnesha
yes right |dw:1443017933992:dw| and then 4(x+4) = 4x +16 now combine like terms
Nnesha
  • Nnesha
x^2 +4x is correct :=)
anonymous
  • anonymous
ohh ok Thanks!
Nnesha
  • Nnesha
|dw:1443018028522:dw|alright now combine like terms
Nnesha
  • Nnesha
do you know what are `like terms ` ?
anonymous
  • anonymous
no :C
anonymous
  • anonymous
i beilive they are x2 and 16 4x and 4x
Nnesha
  • Nnesha
hmm like terms that contains same variables
Nnesha
  • Nnesha
x^2 is same as 1x^2 so 16 and 1x^2 are the same ?
Nnesha
  • Nnesha
there is a variable with 1 but no variable with 16
anonymous
  • anonymous
hmm so what dose that mean?
Nnesha
  • Nnesha
hmm like terms that contains the same variable so 1x^2 and 16 are like terms or not ?
anonymous
  • anonymous
no coreect?
Nnesha
  • Nnesha
yes right so just combine 4x+4x just add the coefficient here is an example 2x+4x=(2+4)x =6x
anonymous
  • anonymous
well 4x+4x is 8x
Nnesha
  • Nnesha
yes right \[-32=-2(x^2+8x+16)\] now distribute parentheses by -2
Nnesha
  • Nnesha
|dw:1443018609249:dw|
anonymous
  • anonymous
umm ... i got 0,-8
anonymous
  • anonymous
same as my answer from before so is it correct?
Nnesha
  • Nnesha
ohh well i was just asking abt -2(x^2+8x+16) but yes that is the answer if u use calculator not gonna force u to work by hand :D
anonymous
  • anonymous
sorry iys touch im bad at numbers
anonymous
  • anonymous
Sorry my its just im bad at numbers*
anonymous
  • anonymous
so the asnwer to my origanal problem is 0,-8
anonymous
  • anonymous
thanks
Nnesha
  • Nnesha
yw
anonymous
  • anonymous
err 0,-8 was inccorect on my question
anonymous
  • anonymous
yeet
Nnesha
  • Nnesha
are the solution you should write in two order pair (x1,y1)(x2,y2)
Nnesha
  • Nnesha
remember x-intercept when y =0 so when x=0 y=0 for 2nd order pair when x=-8 y=0

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