# What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for y=x^2+12x-9?

May 12, 2015

x of axis of symmetry and vertex:
x = -b/2a = -12/2 = -6. y of vertex:
y = f(-6) = 36 - 72 - 9 = -45

Since a = 1, the parabola opens upward, there is a minimum at
(-6, 45).
x-intercepts: $y = {x}^{2} + 12 x + 9 = 0.$

$D = {d}^{2} = 144 + 36 = 180 = 36.5 \to d = \pm 6 s q r 5$

Two intercepts:
$x = - 6 + \frac{6 s q r 5}{2} = - 6 + 3 s q r 5$
$x = - 6 - \frac{6 s q r 5}{2} = - 6 - 3 s q r 5$