Question

Lef f(x)=Ax^2+Bx+C. If f(1)=3, f(-1)=7, and f(0)=4, what are the values of A, B, and C?

Answer 1

well if f(0) = 4.....then let x=0, ->C = 4 ................f(1) = 3, let x = 1 -> A+B +4 = 3 --> A+B =-1.......f(-1)=7, let x= -1 -->A-B +4 = 7 --> A-B = 3 ............solve A and B using substitution

Answer 2

Theres something random i read in a book called "Linear Interpolation", i wonder if that could solve this....ima try.

Answer 3

using Linear Interpolation im getting:
\[f(x) = x^2-2x+4\], is that what answer everyone else is getting doing it the normal way?

Answer 4

i'll post a solution if it matches.

Answer 5

yes that matches...A=1, B=-2, C = 4

Answer 6

nice, alright, let me scan my work.