calculusxy
  • calculusxy
MEDAL! I need help on transformation \(y = x^2 - 8x + 12\)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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calculusxy
  • calculusxy
@satellite73
calculusxy
  • calculusxy
@SolomonZelman
anonymous
  • anonymous
transform in to what?

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anonymous
  • anonymous
vertex form maybe?
calculusxy
  • calculusxy
no it's how it will transform from y = x^2
anonymous
  • anonymous
same thing as writing in vertex form
calculusxy
  • calculusxy
my vertex form was \((x - 4)^2 -4 \)
anonymous
  • anonymous
half of 8 is 4 so it it going to look like \[y=(x-4)^2+k\] to find \(k\) replace \(x\) by \(4\)
anonymous
  • anonymous
ok i believe you
anonymous
  • anonymous
that means it is shifted how?
calculusxy
  • calculusxy
i know that the a part is whether the parabola faces up or down (is there is a mathematical term for this?)
anonymous
  • anonymous
you have two \(-4\)'s there the one inside means shifted RIGHT 4, the one outsides means DOWN 4
anonymous
  • anonymous
it faces up because the leading coefficient is positive (it is 1)
calculusxy
  • calculusxy
i know that the a part is whether the parabola faces up or down (is there is a mathematical term for this?)
calculusxy
  • calculusxy
the h part (horizontal translation) do i have to look at -4 or 4 (the one that will replace x to get 4 - 4 = 0 ?
anonymous
  • anonymous
the vertex of \(y=x^2\) is \((0,0)\) and the vertex of \(y=(x-4)^2-4\) is \((4,-4)\) so you see the shift a) right 4 b) down 4
anonymous
  • anonymous
i guess you should think "look at the 4" in the\((x-4)^2\) part right 4, not left 4
anonymous
  • anonymous
so yes, the one that you replace x by to get 0
calculusxy
  • calculusxy
so i look at -4?
anonymous
  • anonymous
4
anonymous
  • anonymous
vertex is \((4,-4)\)
calculusxy
  • calculusxy
okay. so that means that the horizontal translation will move 4 spaces to the left and the vertical translation will move 4 spaces down (since k is -4)?
anonymous
  • anonymous
no
anonymous
  • anonymous
horizontal translation os 4 units to the RIGHT
anonymous
  • anonymous
how do you get from the vertex of \(y=x^2\) with is \((0,0)\) to the vertex of \(y=(x-4)^2-4\) which is \((4,-4)\)?
calculusxy
  • calculusxy
can u give me the rules for horizontal translation?
anonymous
  • anonymous
i think of it like this compared to the graph of \(y=f(x)\) the graph of \(y=f(x+h) \) is shifted LEFT if \(h\) is positive, like \(f(x+3)\) would shift it 3 units left it is shifted RIGHT if \(h\) is negative, for example \(f(x-2)\) is shifted 2 units right
calculusxy
  • calculusxy
okay i got it. so the transformations are: 1) the parabola is going to face up 2) the horizontal translation is 4 spaces to the right because it is positive 4 3) the vertical translation is 4 spaces down because it is -4
anonymous
  • anonymous
for quadratics some books write it like this: the vertex of \[y=a(x-h)^2+k\] is \((h,k)\)
anonymous
  • anonymous
right, what you said
calculusxy
  • calculusxy
thanks!
anonymous
  • anonymous
yw

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