Question

Given the following absolute value equation, what would the coordinates of the vertex be?

​ y= -3 |x-5| +2
A (−5,2)(-5,2)(−5,2)
B (−3,−5)(-3,-5)(−3,−5)
C 5,2)(5,2)(5,2)
D (2,−5)(2,-5)(2,−5)

Answer 1

C. (5,2)

Explanation:

For parent function f(x) with vertex at (0, 0), translating it horizontally by "h" and vertically by "k" makes it look like

f(x -h) +k

and the vertex moves to (h, k).

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Here, the parent function |x| has its vertex at (0, 0). Writing it as ...

-3|x -5| +2

moves its vertex to (h, k) = (5, 2).

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Additional comment

The factor -3 serves to reflect the graph over the x-axis and expand it vertically by a factor of 3. It has no effect on the translation of the vertex.