Find the quadratic function fx whose graph passes through 1

Find the quadratic function f(x) whose graph passes through (1, -3) and (-2, 21) and such that f\'(-1) = -10. You may use your calculator. Show any systems, their augmented matrices, and their RREF matrices. Be sure to give your final answer in f(x) = ax^2 +bx + c form.

Solution

y=ax²+bx+c as the graph passebbbs through ( 1 ,-3) (-2,21) hence -3=a+b+c --(1) 21=4a-2b+c ----(2) -10=a- b+c----(3) The augumented Matrics and their RRFF Matrics are Mat 1 1 1 Mat a -3 4 -2 1 b = Mat 21 1 -1 1 c -10 from(1) &(2)we get a-b=8---(4) from (2)&(3) we get 3a-b=31---(5) solving(4)&(5) we get a=23/2 &b=7/2 putting the values of b&c in eqn (1) we get c=-18 putting the values of a b &c in y=ax²+bx+c we get y=23/2x²+7/2x-18 ANS