Answer:
[tex]f(x)=2(x+4)^2-27[/tex]
Step-by-step explanation:
Complete the square
[tex]f(x)=2x^2+8x+5\\f(x)=2(x^2+8x+\frac{5}{2})\\f(x)+2(\frac{27}{2})=2(x^2+8x+\frac{5}{2}+\frac{27}{2})\\f(x)+27=2(x^2+8x+16)\\f(x)+27=2(x+4)^2\\f(x)=2(x+4)^2-27[/tex]
This tells us that the vertex of the parabola is [tex](-4,-27)[/tex].
