Question

PLEASEE could someone help me with this and show work

Answer 1

Answer:

Axis of symmetry: $x=-3$

Vertex: $(-3,-5)$

Step-by-step 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 $(-3,-5)$

Answer 2

Answer:

the vertex is ( - 3,  - 5)

Step-by-step 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)