Answer: a=2 b=5 c=-7
parabola equation is y = 2x^2+5x-7 = 0
Explanation:
Substitute (x,y) into y = a x^2 + b x + c
(2,11) 11 = 4a + 2b + c
(-1,-10) -10 = a - b + c
(-4,5) 5 = 16a -4b + c
Solve the linear system in a, b, c
Det[{{4,2,1},{1,-1,1},{16,-4,1}}] = 54
Det[{{11,2,1},{-10,-1,1},{5,-4,1}}] = 108
Det[{{4,11,1},{1,-10,1},{16,5,1}}] = 270
Det[{{4,2,11},{1,-1,-10},{16,-4,5}}] = -378
a = 108/54 = 2
b = 270/54 = 5
c = -378/54 = -7
parabola equation is y = f(x) = 2x^2+5x-7
f(2) = 8+10-7 = 11 ✔
f(-1) = 2-5-7 = -10 ✔
f(-4) = 32-20-7 = 5 ✔