Given:#" "y=x^2-8x+18" ..........................Equation(1)"#

#color(brown)("Assumption: by 'graphing form' you mean completing the square")#

Let #k# be an error correction value.

Write as:

#y=(x^2-8x)+18 +k#

Take the power outside the brackets

#y=(x-8x)^2+18+k#

Halve the #8x#

#y=(x-4x)^2+18+k#

Remove the #x# from #4x#

#y=(x-4)^2+18+k" .....................Equation(2)"#

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#color(brown)("Explanation about dealing with the error")#

So we have now progressed from #ax^2+bx+c#

to #a(x+b/(2a))^2+c+k larr" equation(2) generalised"#

but in this case #a=1#

If we were to square out the brackets what we end up with would include #" "a(b/(2a))^2" "# which is the error so we have to set

#a(b/(2a))^2+k=0" "# to get rid of the error.

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In your question the error is #1xx(-4)^2#

Remember that #a=1# from #color(green)(color(red)(1x^2)-8x+18)#

So we set #(-4)^2+k=0 => k=-16#

Thus Equation(2) becomes

#y=(x-4)^2+18-16#

#y=(x-4)^2+2#