Verified Answer :

\(f(x) =x^{2} +8x+3 \\ f(x) =a(x-p)^{2} +q =(x+4)^{2}-13 \\ a=1 \\ p= \frac{-b}{a} =- \frac{8}{2} =-4 \\ q=f(p) =f(-4)=(-4)^{2} +8 \cdot (-4)+3=16-32+3=-13\)

Answer and workings can be found in the attachment below...

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