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Parabolas

Parabolas. Objective: Be able to identify the vertex, focus and directrix of a parabola and create an equation for a parabola. Thinking Skill: Explicitly assess information and draw conclusions. Warm Up: Please pick up the three sheets on the podium & complete the half sheet warm-up.

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Parabolas

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  1. Parabolas Objective: Be able to identify the vertex, focus and directrix of a parabola and create an equation for a parabola. Thinking Skill: Explicitly assess information and draw conclusions Warm Up: Please pick up the three sheets on the podium & complete the half sheet warm-up.

  2. Parabola • Definition: All the points (x, y) equidistant from a fixed line (directrix) and a fixed point (focus) • Standard form • Vertical – Horizontal Directrix: y = k – p Directrix: x = h – p Where the vertex is (h, k) and p is the directed distance to the focus.

  3. Parabola Examples • Find the equation of the parabola with a vertex of (5, 2) and a focus of (3, 2) Standard Form: General Form:

  4. Parabola Examples • Find the equation of the parabola with a focus of (-2, 3) and a directrix of y = 7 Standard Form: General Form:

  5. Parabola Examples • Find the focus, vertex & directrix of the parabola x = 0.125y2 + 0.25y + 0.125 and graph the parabola.

  6. Reflective Property The tangent line to a parabola at a point P makes equal angles with the following two lines • The line passing through P and the focus • The axis of the parabola P

  7. Find the equation of the tangent line to the parabola given y = x2 at the point (1,1)

  8. Closing Problem • Find the vertex, focus and directrix of y = ¼ (x2 – 2x + 5) • Vertex ( 1, 1) • Focus (1, 2) • Directrix y = 0

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