Use a system of equations to find the equation of the parabola y = ax^2 + bx + c that passes through the points. Solve the system using matrices. Use a graphing utility to verify your result.

Question

The points are (1,6), (4,3), (5,-2)

Answer 1

using (1,6) ---> 6 = a + b + c
using (4,3) ---> 3 = 16a + 4b + c
using (5,-2) ---> -2 = 25a + 5b + c
The 2nd minus the first: 15a + 3b = -3 or 5a + b = -1
the 3rd minus the 2nd: 9a + b = -5
Now subtract those last two:
4a = -4
a = -1
sub that into 5a + b = -1 to get b
then go into the very first one to get c

Answer 2

@reiny thanks but how did you get 16a in 3 = 16a + 4b + c and 25a in -2 = 25a + 5b + c

Answer 3

your equation is y = ax^2 + bx + c
so in (4,3), x = 4, and y = 3
so 3 = a(4^2) + b(4) + c

same for the other points

Answer 4

thanks, now i get it