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Answer:
vertex: (-3, 3)
focus: (-3, 2)
directrix: y = 4 (the line)
point on the parabola: (1, -1)
Step-by-step explanation:
The vertex is the extreme point of the parabola. For a parabola opening downward, it is the maximum. Here, that point is labeled (-3, 3).
The focus is a point inside the parabola on the line of symmetry that, together with the directrix, helps define the parabola. Every point on the parabola is the same distance from the focus as it is from the directrix. Here, the point (-3, 2) is the focus.
The directrix is a line outside the parabola that is the same distance from the vertex that the focus is inside. Here, that line is y = 4.
The point on the parabola (1, -1) appears to have no particular significance. It happens to be 5 units distance from both the focus and the directrix.
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<em>Additional comment</em>
When you draw a horizontal line through the focus, it intersects the parabola at a point the same distance from the focus as from the directrix. (All points on the parabola have that characteristic. This point just happens to have the same y-coordinate as the focus.) The point you found this way is also on a line through the vertex that has a slope of 1/2 or -1/2.
If you don't know where the focus is for a given parabola, you can always find it using this relationship.
, where r is the radius of the base and l is the slant height.
