find minimum y-value

Question

Find the minimum y-value on the graph of y=f(x)

 

F(x)=x²+6x+5

 

Please help..thank you

Answer 1

Minimum:

              ( ( - b/2a, f( -b/2a) )

 

      f( -b/2a) = ( -6/ 2) ^2 +6 ( -6/2) + 5

 

                   = 9  - 18 + 5 = -4

Answer 2

complete the square on the equation. If you do the equation is now (X2+6x+9)-4. This is y=(x+3)2-4

 

The vertex is at x=-3, y=-4