Question

can someone take me step by step on how to write a quadratic model for given points?

Answer 1

example: (1,-1) (2,-5) (3,-7)

Answer 2

ok look at the x portion of the points, 1 2 3 so that's just changing on an interval of 1, so bow we want to look at how the y is changing -1 -5 -7 = -4 then -2, guessing that next would be -1 then -1/2 ...

Answer 3

okk

Answer 4

whats next

Answer 5

let's change directions, we want a solution in the form ax²+bx+c=y
so let's plug in coordinates and see what we get then solve a system of equations

Answer 6

so for the first coordinate we get a(1)²+b(1)+c=(-1) solve for c and we get -c=a+b+1
for point 2 we get a(2)²+b(2)+c=(-5) solve for c we get -c=4a+2b+5 set the equations equal and we get a+b+1=4a+2b+5 simplify and solve for a and we get a=(-4-b)/3 moving to the last point a(3)²+b(3)+c=(-7) = 9a+3b+c=-7 and i got lost somewhere in here lol

Answer 7

three equations 3 unknowns:
a+b+c=-1
4a+2b+c=-5
9a+3b+c=-7

Answer 8

if you know how to use matrices you can solve it that way. a=1,b=-7, c=5 so ax²+bx+c=y would be x²-7x+5