Question

PLEASEE could someone help me with this and show work

Answer 1

the vertex is ( - 3, - 5)

Explanation:

y = 2x² + 12x + 13

let a=2, b=12, c= 13

Xv = - 12 /(2*2)

Xv = -3

Yv = -5

therefore the vertex is ( - 3, - 5)

Answer 2

Axis of symmetry:
`x=-3`

Vertex:
`(-3,-5)`

Explanation:

The given equation is
`y=2x^2+12x+13`

We complete the square to get the function in the vertex form.

`y=2(x^2+6x)+13`

`y=2(x^2+6x+9)-2*9+13`

`y=2(x+3)^2-18+13`

`y=2(x+3)^2-5`

We compare to
`y=a(x-h)^2+k`

We have a=2,h=-3 and k=-5

The equation of axis of symmetry is x=h

i.e
`x=-3`

The coordinate of the vertex is (h,k) i.e
`(-3,-5)`