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: Look over your Unit 9 test.

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.

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 = 0.125y2 + 0.25y + 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 The line passing through P and the focus The axis of the parabola P

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

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