Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Complete the square

$f(x)=2x^2+8x+5\\f(x)=2(x^2+8x+\frac{5}{2})\\f(x)+2(\frac{27}{2})=2(x^2+8x+\frac{5}{2}+\frac{27}{2})\\f(x)+27=2(x^2+8x+16)\\f(x)+27=2(x+4)^2\\f(x)=2(x+4)^2-27$

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