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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 \[3,5,7,9\]
x -2 -1 0 1 2 h(x) 14 5 2 5 14
are the numbers
would i use successive differences for x or h(x) i think its h(x)
symmetry about y-axis
f(x) = f(-x) even function
do those points fit some parabola, quadratic?
yes it makes a parabola
h(x) = a*x^2 + b*x + c you can use the data points to figure the constants
what value do i put in for a, b and c
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
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
Sorry i can help now
i have to run, but do that, and solve the sytem for a and b looks like h(x) = 3x^2 + 2
b turns out to be 0
which it should
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
could that also be a periodic function with limited domain..
successive odd numbers means it is a square
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 \((x+?)^2+2\)
ok that was wrong!!
i see, never knew that differences term meaning
it is going to be \[a(x+h)^2+2\]
i know what you meant .
yeah like successive differences for \(x^2\) are (for positive values) 1,3,4,5,7...
it only says "classify" not "find" although @dan815 answered that it if really only says "classify" you could say "quadratic"
oops wrong dan
for x a unit to the right
@DanJS answered that
the successive differences is -9,-3, +3, +9 right?
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
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.
14 5 2 5 15 -9 -3 3 9 6 6 6 <--- second difference tier is constant at 6
yeah, just read that, was gonna say something about the derivative of p(x), and how many to get to a constant
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
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
forgot to to tack on the c = 2 at the end
14 = 4*a + 2
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
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).
a*x^n term, the a = constant/n!
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
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! ..