SOLUTION: Where will the vertices of the graphs of y = |2x-7| - c if c is any real number?

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Question 1012906: Where will the vertices of the graphs of y = |2x-7| - c if c is any real number?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
The vertex (the only vertex) of the graph y = |2x-7| - c is there

where 2x - 7 = 0, i.e. at x = 7%2F2 = 31%2F2.

See the figure below.




Figure. Plot of y = |2x-7| - 1


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Where will the vertices of the graphs of y = |2x-7| - c if c is any real number?
This is a piece-wise function, with standard form being: y+=+a%2Aabs%28x+-+h%29+%2B+k, where (h, k) is the vertex

RETRACTION!



The coefficient of x in the piece-wise function is > 1, so to get the equation of the piece-wise function, the equation becomes: y+=+2+%2A+abs%28x+-+7%2F2%29+-+c. 

Therefore, the vertex, or (h, k) is at the coordinate point: highlight_green%28matrix%281%2C4%2C%22%28%22%2C7%2F2%2C%22%2C%22%2C%22-+c%29%22%29%29, which places the vertex in the 4th quadrant where h or the

x-coordinate is > 0, and k, or the y-coordinate is < 0