Answer:
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
