The graph of a certain quadratic y = ax^2 + bx + c is a parabola with vertex (-4,0) which passes through the point (1,-75). What is the value of \(a\)?
\(\text{Writing this in vertex form we have}\\ y = \alpha(x+4)^2 + 0 = \alpha(x+4)^2\\ \text{using the point we're given}\\ -75 = \alpha(1+4)^2 = 25\alpha\\ \alpha = -3\\~\\ y = -3(x+4)^2 = -3(x^2 + 8x+16)\\ y = -3x^2 - 24x - 48\\ a = -3\)
\(\text{Writing this in vertex form we have}\\ y = \alpha(x+4)^2 + 0 = \alpha(x+4)^2\\ \text{using the point we're given}\\ -75 = \alpha(1+4)^2 = 25\alpha\\ \alpha = -3\\~\\ y = -3(x+4)^2 = -3(x^2 + 8x+16)\\ y = -3x^2 - 24x - 48\\ a = -3\)
