Answer:
Vertex form [tex]f(x) =(x +2)^2 +4[/tex]
The vertex is [tex](-2,4)[/tex]
Step-by-step explanation:
For a general quadratic function the form is:
[tex]ax ^ 2 + bx + c[/tex]
For the function
[tex]f(x) = x ^ 2+ 4x +8[/tex]
The values of the coefficients for the function are the following: [tex]a = 1[/tex], [tex]b =4[/tex], [tex]c = 8[/tex]
Take the value of b and divide it by 2. Then, the result obtained squares it.
[tex]\frac{b}{2}= \frac{4}{2}[/tex]
[tex](\frac{b}{2})^2=(2)^2=4[/tex]
Add and subtract 4
[tex]f(x) = (x ^ 2 +4x +4) + 8- 4[/tex]
Write the expression of the form
[tex]f(x) = (x+\frac{b}{2})^2 +k[/tex]
[tex]f(x) =(x +2)^2 +4[/tex]
The vertex is [tex](-2,4)[/tex]
