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

It has minimum at x = -1

so it is of the form

f(x) = m(x+1)^2 + n


x = - 1 gives n = - 5


so f(x) = m(x+1)^2 - 5

at x = -2 it is zero so 0 = m- 5 => m= 5

so f(x) = 5 (x+1)^2 - 5 = 5x^2 + 10x

so a= 5 and b= 10 and c = 0