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Unformatted text preview: −2). We also see that 4p = −8 so that p = −2.
Since p < 0, the focus will be the left of the vertex and the parabola will open to the left. The
distance from the vertex to the focus is |p| = 2, which means the focus is 2 units to the left of 1, so
if we start at (1, −2) and move left 2 units, we arrive at the focus (−1, −2). The directrix, then, is
2 units to the right of the vertex, so if we move right 2 units from (1, −2), we’d be on the vertical
line x = 3. Since the focal diameter is |4p| is 8, the parabola is 8 units wide at the focus, so there
are points 4 units above and below the focus on the parabola.
−1 1 2 x −2
−6 In studying quadratic functions, we have seen parabolas used to model physical phenomena such as
the trajectories of projectiles. Other applications of the parabola concern its ‘reﬂective property’
which necessitates knowing about the focus of a parabola. For example, many satellite dishes are
formed in the shape of a para...
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