Question

2. Use successive differences to classify the function represented in the table.


I don't know what they're asking for could someone describe it to me

Answer 1

the table would help
but "successive differences" means subtract the previous output from the next one
for example, the successive differences for \[1,4,9,16\] are \[3,5,7,9\]

Answer 2

x -2 -1 0 1 2

h(x) 14 5 2 5 14

Answer 3

are the numbers

Answer 4

would i use successive differences for x or h(x) i think its h(x)

Answer 5

@satellite73

Answer 6

symmetry about y-axis

Answer 7

f(x) = f(-x)

even function

Answer 8

do those points fit some parabola, quadratic?

Answer 9

yes it makes a parabola

Answer 10

h(x) = a*x^2 + b*x + c

you can use the data points to figure the constants

Answer 11

what value do i put in for a, b and c

Answer 12

you use the points (x,h(x)) in the table to figure it, at most 3 points are needed, but they gave you x=0, and there h(0) = c = 2

Answer 13

h(x) = ax^2 + bx + 2

set up 2 equations using 2 points on the table, not x=0

solve that for a and b

Answer 14

Sorry i can help now

Answer 15

i have to run, but do that, and solve the sytem for a and b

looks like

h(x) = 3x^2 + 2

Answer 16

b turns out to be 0

Answer 17

ok

Answer 18

which it should

Answer 19

14 = a*(-2)^2 + b*(-2) + 2

for example, using (x , y) = (-2, 14)

choose one more, solve that pair for a and b

a=3 b=0

Answer 20

could that also be a periodic function with limited domain..

Answer 21

successive odd numbers means it is a square

Answer 22

true it could actually be anything, but they want you to say it is a square
the fact that \((0,2)\) is on the graph means it is going to be \((x+?)^2+2\)

Answer 23

ok that was wrong!!

Answer 24

i see, never knew that differences term meaning

Answer 25

it is going to be \[a(x+h)^2+2\]

Answer 26

i know what you meant .

Answer 27

yeah like successive differences for \(x^2\) are (for positive values)
1,3,4,5,7...

Answer 28

it only says "classify" not "find" although @dan815 answered that
it if really only says "classify" you could say "quadratic"

Answer 29

oops wrong dan

Answer 30

for x a unit to the right

Answer 31

@DanJS answered that

Answer 32

the successive differences is -9,-3, +3, +9 right?

Answer 33

yeah, some property satellite said about strings of increasing odd being prabolas, i never heard any of that, have to test it, or look it up

Answer 34

the number of tiers it takes to get to a constant difference (think derivatives) tells us something about the original sequence.

quadratic functions have 2 difference tiers (their 2nd derivative) is a constant.

Answer 35

14 5 2 5 15
-9 -3 3 9
6 6 6 <--- second difference tier is constant at 6

Answer 36

yeah, just read that, was gonna say something about the derivative of p(x), and how many to get to a constant

Answer 37

is this correct?


Y=ax^2+bx+c
14=a(-2)^2
14=a(4)
We then divided 4 by both sides
A=3.5 or 3 ½
So y= 3 ½ x^2

Answer 38

since they show the vertex point, change in dec or inc value, you get the c value for free,
and you can also use that vertex formula

Answer 39

forgot to to tack on the c = 2 at the end

Answer 40

14 = 4*a + 2

Answer 41

y = a*(x-h)^2 + k

y = a*(x - 0)^2 + 2

--------------------if you dont have the vertex (h,k), then you have to do the old way, solve a system probably

Answer 42

here is something interesting...

If you take n successive differences before you get a constant difference, then the degree of the polynomial is n, and the coefficient of the xn term is that constant difference divided by n! (that is, n factorial).

Answer 43

a*x^n term, the a = constant/n!

Answer 44

the constant difference came to 6 after two times doing differences n=2, quadratic , and the value of a on the x^2 is 6/2! = 3

nice little shortcut if you remember

Answer 45

x^u
u*x^(u-1)
u*(u-1)*x^(u-2)

makes sense, to get the 'a' term thing, application of changing derivatives
u!

..