Let's first rewrite it in vertex form.
Start by completing the square.
y = x² + 4x + 4 - 4 - 1
y = (x + 2)² - 5
(x + 2)² = y + 5
Now, 4a = 1; a = [tex] \frac{1}{4} [/tex]
So, the vertex form is (x + 2)² = 4([tex] \frac{1}{4} [/tex])(y + 5)
So, we know that the vertex is at (-2, -5).
Since it's a concave up parabola, we just have to change the y-value to find the focus.
∴ F(-2, -5 + [tex] \frac{1}{4} [/tex])
F(-2, [tex] \frac{-19}{4} [/tex])
