Given f(x)=x^2+8x+13. enter the quadratic function in vertex form in the box f(x)=

i need and show me the work

f(x) = (x + 4)² - 3

Step-by-step explanation:

The equation of a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² + 8x + 13

To obtain f(x) in vertex form use the method of completing the square

add/ subtract (half the coefficient of the x- term)² to x² + 8x

f(x) = x² + 2(4)x + 16 - 16 + 13

f(x) = (x + 4)² - 3 ← in vertex form

it would open into a square depending on the type of envelope i’m not sure about the second part