A. Directrix ⇒ y = 4 B. Focus ⇒ (-3, 2) C. Vertex ⇒ (-3, 3)
How do we identify these point for the given parabola?
1. The directrix of a parabola is a line perpendicular to the axis of symmetry that does not touch the parabola itself. Therefore the horizontal line above the vertex is the directrix. The coordinate starts at (-7, 4) up to (7, 4). Therefore y = 4
2. The focus of a parabola is a point from which distances to any point on the parabola and the nearest point on the directrix are equal. Since the parabola opens downwards, it lies below the vertex.
y=3 to y=4, so the focus would also be 1 unit below the vertex, at (−3,3−1) which is (−3,2).
3. Vertex: The highest or lowest point on a parabola is the vertex. According to the given parabola, the peak point is (-3, 3).