Parabolas

Unit Vocabulary Focus- A point that lies on the axis of a parabola, p units from the vertex. Directrix- line that “underlines” a parabola. Parabola- Set of all points equidistant from a point called the focus and a line called the directrix.

Standard Form: Given on formula sheet: y – k = (x – h)2 or x – h = (y – k)2 You are going to change these….. Multiply both sides by 4p 4p(y – k) = (x – h)2 and 4p(x – h) = (y – k)2 YAY!!! NO more fraction!!!

VERTICAL vs. HORIZONTAL Opens Vertically Horizontally Standard Equation 4p(y – k) = (x – h)2 4p(x – h) = (y – k)2 Axis of Symmetery x = h y = k Direction If p > 0 opens up If p < 0 opens down If p > 0 opens right If p < 0 opens left Vertex (h, k) Focus (h, k + p) (h + p, k) Directrix y = k - p x = h - p

Find the vertex of the following parabolas and tell which direction they are opening. 1. (x – 3) = (y + 2)2 2. (y + 4) = (x - 9)2 3. (x + 6) = (y + 5)2 4. (y – 7) = (x - 11)2

Find the equation of a parabola with the given focus and directrix focus (-5, 0) and directrix x = 5 focus (12, 0) and directrix x = -12 focus (0, -4) and directrix y = 4 focus (2,2) and directrix y = -2

Find the focus and the directrix of the following parabolas. y – 2 = (x + 7)2 x – 6 = (y - 1)2 x – 7 = (y + 8)2 y + 3 = (x + 1)2

Ex. Write the equation of the function in the graph below 9. Directrix y = 2 10. focus at (-5, -4)

Homework Parabolas Worksheet