Here is how the equation x = a(y-k)^2 + h represents the standard form for a parabola:
vertex: The vertex of the parabola is the point (h, k). This is the point where the parabola turns around.
directrix: The directrix is the line x = h.
focus: The focus is the point (h, k - 1/(4a)).
axis of symmetry: The axis of symmetry is the vertical line x = h. It passes through the vertex and is perpendicular to the directrix.
So in summary:
- The vertex (turning point) of the parabola is (h, k)
- The directrix is the line x = h
- The focus is the point (h, k - 1/(4a))
- The axis of symmetry is the vertical line x = h, passing through the vertex
- The parameter a determines how "wide" or "narrow" the parabola is
Hope this breakdown helps! Let me know if you have any other questions.