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

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

3. 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

4. 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

5. 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)

6. 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.

7. 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.

8. 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

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