Answer:
[tex]y=2(x+2) ^ 2 + 2.[/tex]
Step-by-step explanation:
For a quadratic equation written in the general form [tex]y=ax ^ 2 + bx + c[/tex],
the x coordinate of its vertex is:
[tex]x = -\frac{b}{2a} = h[/tex]
Then this equation written in the form of vertex is:
[tex]y=a(x-h) ^ 2 + k.[/tex]
Where the point (h, k) is the vertex of the parabola.
In this case we have the equation
[tex]y=2x^2+8x+10[/tex]
Then the x coordinate of its vertex is:
[tex]x=-\frac{8}{2(2)}\\\\x= -2[/tex]
Therefore the y coordinate of its vertex is:
[tex]f(-2) = 2(-2)^2+8(-2)+10\\\\f(-2) = 2[/tex]
The vertice is (-2, 2)
Then
[tex]h=-2\\\\k = 2[/tex].
This equation written in the form of vertex is
[tex]y=2(x+2) ^ 2 + 2.[/tex]
