Answer:
[tex]y = {(x + 3)}^{2} - 14[/tex]
Step-by-step explanation:
The original equation
[tex] f(x) = {x }^{2} + 6x - 5[/tex]
vertex form
[tex]y = a {(x - h)}^{2} + k \\ where \: (h. \: k) \: is \: the \: vertex[/tex]
solve for the x coordinate of the vertex, h
[tex]x = h = - \frac{b}{2a} = - \frac{6}{2(1)} = - \frac{6}{2} = - 3 \\ x = h = - 3[/tex]
substitute -3 back into the original equation to solve for y
[tex]y = { (- 3)}^{2} + 6( - 3) - 5 \\ y = 9 - 18 - 5 \\ y = 4 - 18 \\ y = k = - 14 [/tex]
substitute h and k values into the vertex form
a = 1 So we can omit it
[tex]y = {(x - ( - 3)}^{2} - 14 \\ y = {(x + 3)}^{2} - 14[/tex]
