What is the nth term of the quadratic sequence: -8,-8,-6,-2,4,12,22?

quadratic sequence

seems to be

where , and so on

we only need 3 points

(1,-8)

(2,-8)

(3,6)

subsitute and solve

(1,-8)

(2,-8)

(3,6)

so we have

-8=a+b+c

-8=4a+2b+c

6=9a+3b+c

add negative of the first equation to the last 2 equations to get

-8=a+b+c

0=3a+b

14=8a+2b

work with the last 2 equations

0=3a+b

14=8a+2b

multiply 1st equation by -2 and add to 2nd

0=-6a-2b

14=8a+2b +

14=2a+0

14=2a

divide by 2

7=a

sub back

0=3a+b

0=3(7)+b

0=21+b

-21=b

sub back

-8=a+b+c

-8=7-21+c

-8=-14+c

6=c

so a=7, b=-21, c=6

the nth term is

or in function form,

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: