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**thereddevils** If the function ax^2+bx+c has a minimum value -5 when x=-1 and 0 when x=-2 , find the values of a , b and c .

This is what i did :

Let $\displaystyle f(x)=ax^2+bx+c $.. completing the square

$\displaystyle =a[(x+\frac{b}{2a})^2+\frac{4ac-b^2}{4a^2}]$

$\displaystyle =a(x+\frac{b}{2a})^2+\frac{4ac-b^2}{4a}$

$\displaystyle x=-1$ when $\displaystyle y=-5$

$\displaystyle x=-\frac{b}{2a}$ ... b=2a -- 1

$\displaystyle \frac{4ac-b^2}{4a}=-5$ ... 4ac-b^2=-20a -- 2

Combining gives me $\displaystyle ac-a^2=5a$ --3