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Home Limits, Analytic Geometry, and Approximations Parabolas Examples Example 3
 
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Example 3: Finding Vertex, Focus And Directrix

Find the vertex, focus and directrix of the parabola

y = 2x2 - 5x + 4.

First find the point x0 where the slope is 0.

05_limits_g_approx-263.gif

Then

4x0 - 5 = 0,

x0 = 5/4

Substitute to find y0.

y0 = 2(x0)2 - 5x0 +4 = ⅞

The vertex is

05_limits_g_approx-264.gif

We have a = 2, so Ľa = ⅛. By Theorem 2, the focus is

05_limits_g_approx-265.gif

The directrix is

05_limits_g_approx-266.gif

The vertex, axis, focus, and directrix can be used to sketch quickly the graph of a vertical parabola.
Home Limits, Analytic Geometry, and Approximations Parabolas Examples Example 3

Last Update: 2006-11-15