Question

Change the function f(x) = 2x ^ 2 + 8x + 5 into vertex form.

Answer 1

`f(x)=2(x+4)^2-27`

Explanation:

Complete the square

`f(x)=2x^2+8x+5\\f(x)=2(x^2+8x+(5)/(2))\\f(x)+2((27)/(2))=2(x^2+8x+(5)/(2)+(27)/(2))\\f(x)+27=2(x^2+8x+16)\\f(x)+27=2(x+4)^2\\f(x)=2(x+4)^2-27`

This tells us that the vertex of the parabola is
`(-4,-27)`.