Monday, August 5, 2013

When graphing a parabola from an equation in standard form, use these steps:

1.  plot the vertez
2.  plot the focus
3.  draw the directrix line
4.  find the latus rectum
5.  draw the parabola

For example, graph the parabola with the equation (x - 2)^2 = 12(y + 1)

The form of a parabola that opens up or down is in the form (x - h)^2 = 4p(y -k),  the vertex is (h,k), the focus is p units from the vertex in the direction the parabola opens, the directix is the line p units from the vertex in the opposite direction.  The latus rectum is 4p.  Plot a point 2p from the focus in both directions to determine the width of the parabola.

1.  the vertex is (2, -1)
2.  the focus is 3 units from the vertex.. Since p is positive the parabola opens up and the focus is at (2, 2)
3.  the directrix is the horizontal line y = -1
4.  the latus rectum is 12, so move 6 units to the left and right of the focus and plots those points.. The points are (8,2) and (-4,2)
5. now draw the parabola

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