Warm-Up 1. Find the distance between (3, -3) and (-1, 5) 2. Find the midpoint of (4, -6) and (-1, -2)

Graph and Write Equations of Parabolas Section 9-2 Graph and Write Equations of Parabolas

Vocabulary Focus Directrix Vertex Focus – On a parabola, each point is equidistant from this point. Directrix – On a parabola, each point is equidistant from this line. Focus Axis of Symmetry Directrix Vertex

x2 = 4py, p>0 x2 = 4py, p<0 y2 = 4px, p<0 y2 = 4px, p>0 Directrix: y = -p Focus: (0, p) Vertex: (0,0) Vertex: (0,0) Focus: (0, p) Directrix: y = -p x2 = 4py, p>0 x2 = 4py, p<0 Directrix: x = -p Vertex: (0,0) Focus: (p, 0) Vertex: (0,0) Focus: (p, 0) Directrix: x = -p y2 = 4px, p<0 y2 = 4px, p>0

Standard Equation of a Parabola with Vertex at the Origin Equation Focus Directrix Axis of Sym x2 = 4py (0, p) y = -p Vertical (x=0) y2 = 4px (p, 0) x = -p Horizontal (y=0)

Example 1 The equation is in the form y2 = 4px. p = 5 focus = (p, 0) Graph y2 = 20x. Identify the focus, directrix, and axis of symmetry. Step 1: Identify the focus, directrix, & axis of symmetry. The equation is in the form y2 = 4px. p = 5 focus = (p, 0) OR (5, 0) directrix is x = -p OR x = -5 Because y is squared, the axis of symmetry is the x-axis.

Example 1 – Continued Graph y2 = 20x. Identify the focus, directrix, and axis of symmetry. Step 2: Graph – make a T-chart. x y 1 4.5 2 6.3 3 7.7 4 8.9 Step 3: Graph – the directrix. Step 4: Graph – the focus. Step 5: Plot – points.

Example 2 Write an equation of the parabola shown. Focus = (p, 0) (-3, 0) x = 3 p = -3 (- 3, o) y2 = 4px y2 = 4(-3)x y2 = -12x

Homework Section 9-2 Pages 623 –624 3, 4, 9, 11, 12, 16, 26, 27, 29, 30, 32, 38, 40, 41, 45, 55