# What is the discriminant and minimum value for y= 3x^2 - 12x - 36?

Jul 9, 2015

$y = 3 {x}^{2} - 12 x - 36$

#### Explanation:

$D = {d}^{2} = {b}^{2} - 4 a c = 144 + 432 = 576 = {24}^{2}$

Since a > o, the parabola opens upward, there is a minimum at vertex.
x-coordinate of vertex: $x = - \frac{b}{2 a} = \frac{12}{6} = 2$
y-coordinate of vertex: y = f(2) = 12 - 24 - 36 = - 48