Focus and Vertex (1 Viewer)

[Zak Ambrose]

what do these words mean?

the question is

sketch the parabola 16y=x^2, showing clearly the co-ordinates of the focus and vertex.

 

[Drongoski]

The vertex is the turning point of the parabola (y = x² is your most familiar parabola)

The parabola is symmetric and the focus is a special point that lies on its axis of symmetry.



Remember: for upright parabola, vertex (0.0) the standard form for a parabola is:

x² = 4ay (i.e. 4 x a x y)

Here. x² = 16y = 4 x 4 x y

so a = 4
and the focus is (0,a) = (0,4)

So off you go and sketch the graph

 

[studentcheese]

the vertex is the turning point of the parabola. The focus is contained within the parabola, which is the same distance from the vertex as the directrix is the same distance from the vertex.

 

[Zak Ambrose]

here's a nice resource i found which further helped my understanding of focus.
Mathwords: Focus of a Parabola

 

[addikaye03]

the vertex is the turning point of the parabola. The focus is contained within the parabola, which is the same distance from the vertex as the directrix is the same distance from the vertex.

the term is "equidistant", not getting into to you, just to let you know...

My advice is: Graph it! u can get so much from a graph on these type of Q and u dont fuck up the focus point for general parabolas of the form (x-h)^2=4a(y-k)