A function y= ex + f + dx^2 intercepts on the y-axis at point (0,-1). Determine what d, e, and f are when points (1,2) and (-1, -2) lie on the curve.

Answer 1

y= ex + f + dx²

When (0,-1)

ex+f+dx²=y

0+f+0=-1

F=-1

at(1,2)
ex+f+dx²=y

e+f+d=2

e+d=3.......(1)

At(-1, -2)

ex+f+dx²=y

-e+f+d=-2

-e+d=-2+1

-e+d=-1.....(2)

-------------------------------------------------
e+d=3.......(1)
-e+d=-1.....(2)

2d=2

d=1

e=2

I had e,f,d=(2,-1,1)

Answer 2

(0,-1) lies on y= ex + f + dx^2
-1 = 0 + f + 0
f = -1
so y = ex -1 + dx^2
(1,2) lies on y= ex -1 + dx^2 ----> 2 = e -1 + d or e + d = 3
(-1,-2) lies on y= ex -1 + dx^2 --> -2 = -e -1 + d or -e + d = -1
add them :
2d = 2
d = 1
back in 2 = e - 1 + d
2 = e -1 + 1
e = 2

So you have
y = 2x -1 + x^2