SOLUTION: Hi, I'm having trouble with this question from my A level Integration module; Find the equation for a quadratic curve that passes through O(0,0) and its gradient at the poin

Question 924934: Hi,
I'm having trouble with this question from my A level Integration module;
Find the equation for a quadratic curve that passes through O(0,0) and its gradient at the point (-2,3) is -1.
I can integrate a differentiated function to get it's original, but without the differential I'm stuck on this and can't see where to begin.
Thanks,
R
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Quadratic curve :
Passes through the origin :

So,

The derivative of the function is,

The function also passes through (-2,3) where,

1.
But also from the value of the function,

2.
Add eq. 1 to eq. 2,

Then,

So then,

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