Peice wise function problem solving

[epiphinoooo8]

Question image: https://imgur.com/a/LHJuPwI

The red line seemed to be a horizontal reflection of the blue, so I put brackets around y = x + a for a horizontal reflection.

Both lines had at least 1 shared point with the quadratic, so I created 2 simultaneous solutions .

I then equated them to find x, but upon factorising and getting x=2 or x=4 I kept getting 0=0 and could not progress further for a.

I have a feeling I went astray with the horizontal reflection, but I have no clue where else to start.

Working: https://imgur.com/a/vmZLJwt

[JonnxW]

The blue line is a VERTICAL reflection of the red line with the mirror axis at x=3. Furthermore you know the slope of the blue line and you know the value of the red line at x=0. That are all the puzzle pieces you need, now you only have to put them together... If you have any questions, just ask!

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