Question

MEDAL!

I need help on transformation
\(y = x^2 - 8x + 12\)

Answer 1

@satellite73

Answer 2

@SolomonZelman

Answer 3

transform in to what?

Answer 4

vertex form maybe?

Answer 5

no it's how it will transform from y = x^2

Answer 6

same thing as writing in vertex form

Answer 7

my vertex form was
\((x - 4)^2 -4 \)

Answer 8

half of 8 is 4 so it it going to look like \[y=(x-4)^2+k\] to find \(k\) replace \(x\) by \(4\)

Answer 9

ok i believe you

Answer 10

that means it is shifted how?

Answer 11

i know that the a part is whether the parabola faces up or down (is there is a mathematical term for this?)

Answer 12

you have two \(-4\)'s there
the one inside means shifted RIGHT 4, the one outsides means DOWN 4

Answer 13

it faces up because the leading coefficient is positive (it is 1)

Answer 14

i know that the a part is whether the parabola faces up or down (is there is a mathematical term for this?)

Answer 15

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 ?

Answer 16

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

Answer 17

i guess you should think "look at the 4" in the\((x-4)^2\) part
right 4, not left 4

Answer 18

so yes, the one that you replace x by to get 0

Answer 19

so i look at -4?

Answer 20

4

Answer 21

vertex is \((4,-4)\)

Answer 22

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)?

Answer 23

no

Answer 24

horizontal translation os 4 units to the RIGHT

Answer 25

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 \((4,-4)\)?

Answer 26

can u give me the rules for horizontal translation?

Answer 27

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

Answer 28

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

Answer 29

for quadratics some books write it like this:
the vertex of \[y=a(x-h)^2+k\] is \((h,k)\)

Answer 30

right, what you said

Answer 31

thanks!

Answer 32

yw