the graph will minimize when x = .5
it will be symmetric about the line x = .5
the minimum value of y will be y = 4
this occurs when the value of the expression within the absolute value signs is equal to 0.
that occurs when x = .5
since the absolute value of the expression within the absolute value sign can never be less than 0, the graph will bottom out when x = .5 because the expression within the absolute value signs is equal to 0 when x = .5.a
that bottoming out point is where the line of symmetry lies.
all values of y to the left of that line will be equal to all values of y to the right of that line as long as the distance between the x values to the line of symmetry is the same.
for example, when x = 0, the value of the expression within the absolute value signs is equal to -6, but the absolute value of -6 is equal to 6, so y = 6 + 4 = 10 when x = 0.
note that x = 0 is the same distance away from x = .5 as x = 1 is. they are both .5 units away from x = .5.
since x = .5 is the line of symmetry, the value on both sides of that line that are equidistant from that line will be equal.
one of these occurrences is when x = 0 and when x = 1 since they're both equidistance from the line of symmetry.
when x = 1, the value within the absolute value signs is 12 - 6 = 6.
the absolute value of that is 6.
6 + 4 = 10
the value of y is 10 when x = 0 and when x = 1.
