Parabolas Unit 7.1

Conics When the plane cuts a cone at a right angle 4 types:

Parabola in every day life Practical Applications Listening Hand blocking Sun

Location of the parabola on Cartesian plot Why study it? Passing to a teammate: football, basketball, volleyball, shooting a basketball

Last year y = ax 2 + bx + c x = input a = determine positive or negative slope c = y intercept Vertex = -b/2x Roots = -b ± √b 2 – 4ac 2a

This Year (because you are smarter and more ambitious) More detailed Locus – set of all points that fulfill a geometric property Focus – locus of points in a plane that are equidistant from a fixed point Directrix – a specific line Axis of symmetry – line perpendicular to the directrix through the focus Vertex – intersection of the parabola and the axis Parabola – the locus of points in a plane

Parabola

Two types Opens vertically (x – h) 2 = 4p(y – k) Opens horizontally (y – k) 2 = 4p(x – h)

Standard form of equations (x – h) 2 = 4p(y – k) a.Vertex ( h,k) b.Focus (h, k + p) c.Axis of symmetry a: (x = h) d. Directrix d: y = k - p (y – k) 2 = 4p(x – h) a.Vertex (h, k) b.Focus (h + p, k) c.Axis of symmetry a: y = k d. Directrix d: x = h - p

Problem 1 Page 428 (x – 3) 2 = 12(y – 7) 1.Does it open horizontally or vertically? 1.Vertically 2. What are h, p and k 1.h = 3, p = 3, k = 7 3. Vertex: (h, k) or (3, 7) 4.Focus: ( h, k + p) = (3, 10) 5.Axis of symmetry: x = h or 3 6.Directrix: y = k – p; 7 – 3 = 4

Unit 7.1 Problems Page 428 Problems