Find all values of 
such that
has a minimum value of -18.
Please explain thoroughly and very well.
+118609 $$\\y=2(x+4)(x-2p) \qquad p\in R\\
$This is a concave up parabola$\\
$Roots are $ x=-4 \;\;and\;\;x=2p\\
$Axis of symmetry is $ x=(2p+-4)/2 = p-2\\
Min:\\
y=2(p-2+4)(p-2-2p)\\
y=2(p+2)(-2-p)\\
y=-2(p+2)^2\\
$You want this value to be $-18\\
-18=-2(p+2)^2\\
9=(p+2)^2\\
p+2=\pm3\\
p=\pm3-2\\
p=1 \quad or \quad p=-5$$
+118609 $$\\y=2(x+4)(x-2p) \qquad p\in R\\
$This is a concave up parabola$\\
$Roots are $ x=-4 \;\;and\;\;x=2p\\
$Axis of symmetry is $ x=(2p+-4)/2 = p-2\\
Min:\\
y=2(p-2+4)(p-2-2p)\\
y=2(p+2)(-2-p)\\
y=-2(p+2)^2\\
$You want this value to be $-18\\
-18=-2(p+2)^2\\
9=(p+2)^2\\
p+2=\pm3\\
p=\pm3-2\\
p=1 \quad or \quad p=-5$$
