SOLUTION: Obtain the equation of the curve y=ax^2+bx+c,using the following conditions (i) d²y/dx²=2 (ii) The curve is at minimum when x=-1/2 (iii) The curve passes through the point (-2,-

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Obtain the equation of the curve y=ax^2+bx+c,using the following conditions (i) d²y/dx²=2 (ii) The curve is at minimum when x=-1/2 (iii) The curve passes through the point (-2,-      Log On


   

Question 1106926: Obtain the equation of the curve y=ax^2+bx+c,using the following conditions
(i) d²y/dx²=2
(ii) The curve is at minimum when x=-1/2
(iii) The curve passes through the point (-2,- 4).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So, the first derivative is,
dy%2Fdx=2ax%2Bb
and the second is,
d2y%2Fdx2=2a
So,
2a=2
a=1
.
.
.
y=x%5E2%2Bbx%2Bc
Converting to vertex form,
y=%28x%5E2%2Bbx%2B%28b%2F2%29%5E2%29%2B%28c-%28b%2F2%29%5E2%29
y=%28x%2Bb%2F2%29%5E2%2B%28c-%28b%2F2%29%5E2%29
So the minimum occurs at,
-b%2F2=-1%2F2
b=1
.
.
.
y=x%5E2%2Bx%2Bc
.
.
Finally using the point,
-4=%28-2%29%5E2%2B%28-2%29%2Bc
-4=4-2%2Bc
c=-6
.
.
.
highlight%28y=x%5E2%2Bx-6%29