Answer:
f(x) = (x + 4)² - 3
Step-by-step explanation:
The given function is:
f(x) = x² + 8x + 13
The vertex form of the equation of a parabola is:
f(x) = a(x - h)² + k
where (h, k) represents the vertex of the function
Rewrite f(x) = x² + 8x + 13 in the form f(x) = a(x - h)² + k
Add and subtract (8/2)², that is 4², to the function above
f(x) = x² + 8x + 4² + 13 - 4²
f(x) = x² + 8x + 4² + 13 - 16
f(x) = (x + 4)² - 3
Note that f(x) = (x + 4)² - 3 is of the form f(x) = a(x - h)² + k
Therefore, the quadratic function in vertex form is:
f(x) = (x + 4)² - 3