PLEASE HELP! How to reflect this in line x=2 when doing a parabola transformation? (light pencil parabola drawing is just what it'd look like when transformed) please show working too! Thank you so much!

enter image source here

1 Answer

Answer:

The roots:(-2,3) have been transformed to (1,6)

Explanation:

graph{y=(x+2)(x-3) [-20, 20, -10, 10]}
graph{y=(x-1)(x-6) [-20, 20, -10, 10]}

when the graph is needed to be reflected about the line x=2,
the root x=3, is ahead the line x=2 by 1 units, which will be 1 unit behind the line x=2, ie x=1.

2+1=3
2-1=1
Similarly,
the root x=-2, is behind the line x=2 by 4 units, which will be 4 units ahead of the line x-2, ie x=6.

2-4=-2
2+4=6

Distance between x=-2 and x=3 is 5 units
Distance between x=1 and x=6 is 5 units

Thus,
the roots (-2,3), are transformed into (1,6)
#(x=2)(x-3)=0#
is transformed into
#(x-1)(x-6)=0#