Parabolas Objective Be able to identify the vertex

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.

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

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

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

Parabola Examples • Find the focus, vertex & directrix of the parabola x = 0. 125 y 2 + 0. 25 y + 0. 125 and graph the parabola.

Reflective Property The tangent line to a parabola at a point P makes equal angles with the following two lines 1. The line passing through P and the focus 2. The axis of the parabola P

Find the equation of the tangent line to the parabola given y = x 2 at the point (1, 1)

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