Find the QUADRATIc equation 100 POINTS PLS HELP (1,6),(2,19),(3,38),(4,63),(5,94)

Step-by-step explanation:

we are given some coordinates

(1,6),(2,19),(3,38),(4,63),(5,94)

we want to figure out the quadratic equation which passes those coordinates

notice that, the coordinates in quadratic sequence

we know that,

A sequence is quadratic if and only if it has second difference

recall that,

these formulas are necessary to figure out a,b and c

because we know that

Quadratic equation standard form:

therefore to figure out a,b and c these formulas are important

let's figure out a:

we got that 2nd difference is 6 thus

divide both sides by 2

let's figure out b:

by using the second formula we can figure out b

our and are 6 and 19 respectively

substitute:

simplify multiplication:

simplify substraction:

cancel 9 from both sides:

let's figure out c:

our is 6

substitute:

simplify addition:

cancel 7 from both sides:

altogether substitute a,b and c to quadratic equation:

and we are done!

go on the tube you might find some information there

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d