Answer:
y = (x + 2)² + 6
Step-by-step explanation:
To write an equation in vertex form of a parabola with a vertex at (-2, 6), we can use the following formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Vertex form of a quadratic equation}}\\\\y=a(x-h)^2+k\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$(h,k)$ is the vertex.}\\\phantom{ww}\bullet\;\textsf{$a$ is the leading coefficient.}\end{array}}[/tex]
In this case:
Substitute the values of h and k into the formula, and use any value for a. Let's use a = 1:
[tex]y=1(x-(-2))^2+6\\\\y=(x+2)^2+6[/tex]
So, an equation in vertex form of a parabola with a vertex at (-2, 6) is:
[tex]\Large\boxed{\boxed{y=(x+2)^2+6}}[/tex]
