Find the equation of the parabola that goes through the given points.
(1,2) (0,5) (-1,14)
let it be
y = ax^2 + bx + c
from (0,5) ---> 5 = 0+0+c
c = 5
then y = ax^2 + bx + 5
at (1,2)
2 = a + b + 5
a + b = -3 , #1
at (-1,14)
14 = a - b + 5
a - b = 9 , #2
add #1 and #2
2a = 6
a=3
in #1
b = -6
so equation is
y = 3x^2 - 6x + 5
check by making sure each of the given points satisfies the equation.