The coordinates of the focus of the parabola is (-8, 2)
How to find the coordinates of the focus
To find the coordinates of the focus of the parabola given by the equation y = -1/8x² - 2x - 4, we use the standard form of a parabola
y = -ax² + bx + c
The coordinates of the focus are given by (h, k), where
h = -b / 2a and
k is the y-coordinate of the vertex.
For your equation
h = -(-2) / ( 2 * -1/8)
h = -8
solving for k
k = -1/8(-8)² - 2(-8) - 4
k = -8 + 16 - 4
k = 4
The coordinates of the vertex is (-6, 4). The coordinates of the focus in this case is (h, k + 1/4a). Hence we have
(-8, 4 + 1/4(-1/8)
(-8, 4 + 1/(-1/2)
(-8, 4 + (-2))
(-8, 2)
So, the coordinates of the focus are (-8, 2)