1. 10.2
Parabolas

2. 10.2 Parabolas
A parabola is the set of all points (x,y) that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.
Focus (h, k + p)
Vertex (h,k)
Directrix y = k - p

3. Standard Equation of a Parabola
(x - h)2 = 4p(y - k) Vertical axis
Opens up (p is +) or down (p is -)
(y - k)2 = 4p(x - h) Horizontal axis
Opens right (p is +) or left (p is -)

4. left Ex. Find the vertex, focus, and directrix of the parabola
and sketch its graph. y2 + 4y + 8x - 12 = 0
Now complete the square.
y2 + 4y = -8x + 12
y2 + 4y + 4 = -8x
(y + 2)2 = -8x + 16
Write down the vertex
and plot it. Then find p.
(y + 2)2 = -8(x - 2)
4p = -8
p = -2
What does the negative p
mean?
left

5. Directrix
x = 4
V(2,-2)
F(0,-2)
Homework: odd

6. Right, since the axis is vertical, we will be using
Ex. Find the standard form of the equation of the
parabola with vertex (2,1) and focus (2,4).
First, plot the two points.
Which equation will we be using? Vert. or Horz. axis
Right, since the axis is vertical, we will be using
(x - h)2 = 4p(y - k)
What is p?
p = 3
Now write down the equation.
(x - 2)2 = 12(y - 1)