What is the vertex of the graph of y y = l − x + 5 l + 7 y = | − x + 5 | + 7

Question

What is the vertex of the graph of y   y  =  l  −  x  +  5  l  +  7  y  =      |    −  x  +  5      |    +  7

Adelyn Mercado · Accepted Answer

Step 1  y  =      |    5  −  x      |    +  7Consider the absolute value function  f  (  x  )  =      |    x      |  The vertex of the above funciton is (0,0)Consider the following transformation of funcitonsi)   g  (  x  )  =      |    −  x      |  The funciton f(x) has been reflected across the y-axisStep 2ii)   h  (  x  )  =      |    −  (  x  −  5  )      |  The function g(x) has been translated 5 units to the rightStep 3iii)   k  (  x  )  =      |    −  x  +  5      |    +  7The function h(x) has been translated 7 units vertically upwardsTherefore, the vertex is (5,7)The above results can be confirmed from the graph below.

What is the vertex of the graph of y = l -x + 5 l +7y=|−x+5|+7

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