Question 892531
a picture of your graph is shown below.


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.




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