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1. The graph of $y = f(x)$ is a parabola whose vertex is at $(1, -2)$. The graph of $y = f(x - 3)$ is also a parabola. Where is the vertex of the graph of $y = f(x-3)$?

 

2. The graph of $y = f(x)$ has the line $x = 5$ as an axis of symmetry. The graph also passes through the point $(8,-7).$ Find another point that must lie on the graph of $y = f(x).$

 Mar 2, 2021
 #1
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1.    f(x - 3)   just  shits  the parabola to the RIGHT  by  3  units

 

So....the " new "  vertex  after  the shift  is  ( 1  + 3, - 2)  =  (4, -2)

 

 

2.  If  x = 5  is  the  axis of symmetry.......and  (5 + 3, -7)  = (8, -7)  is on the  graph......then ( 5 - 3, -7)   =  (2, -7)  is also on the  graph

 

 

cool cool cool

 Mar 2, 2021

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