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How do you graph and find the vertex for # y=6abs(x-7)#?

Answer 1

Savannah Anderson

#y=6abs(x-7)#

When #x<7# #y = 6(7-x) = 42-6x# which is the equation of a straight line terminating at #(7,0)#

When #x>=7# #y=6(x-7) = 6x-42# which is also the equation of a straight line terminating at #(7,0)#

The vertex is at #(7,0)#

graph{6*abs(x-7) [3.743, 9.902, -0.382, 2.696]}

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Answer 2

Kennedy Adams

To graph the function ( y = 6| x - 7| ) and find the vertex, first, recognize that the absolute value function ( |x| ) is symmetric about the y-axis. Therefore, the graph of ( y = 6| x - 7| ) is a V-shaped graph centered at ( x = 7 ).

The vertex of the absolute value function ( |x| ) occurs at the point (0, 0), but because of the transformation ( x - 7 ), the vertex of ( y = 6| x - 7| ) is at (7, 0).

To graph the function, plot the vertex at (7, 0), and then choose points to the left and right of the vertex, such as (6, 6) and (8, 6), respectively.

As for finding the vertex, it's located at the point (7, 0).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.