This seems disgusting to solve directly, so let's convert this to vertex form.
1) Divide all terms by 1/2:
2y = -x² - 4x + 14
2) Complete the square:
2y = -(x² + 4x - 14)
2y = -(x² + 4x + 4 - 4 - 14)
2y = -[(x + 2)² - 18]
2y = -(x + 2)² + 18
3) Rewrite in vertex form:
(x + 2)² = -2y + 18
(x + 2)² = -2(y - 9)
Now, we know the vertex is at (-2, 9)
It's a concave down parabola
The axis of symmetry is simply the x-ordinate of the vertex.
The focus is at (-2, 17/2)
The directrix is at (-2, 19/2)
The y-intercept is at y = 7
