Page 768, 8-28 even, 58-62even
8) Inconsistent
10) (-1, 2), con and ind
12) (1, 1), con and ind
14) (26/25, -7/25), con and ind
16) Con and dependent
18) (6/5, -6/5)
20) (3/2, 2/3)
22) Infinitely many solutions
24) No solutions
26) (4/5, 1/5)
28) (3, -5)
58) (4, 1.5)
60)
58-62 even
Page 778, 10-30 even
10) (-1, -2, -3)
12) (-2, -1, 3)
14) (-3/2, 1/2, 3/2)
16) Infinitely many
18) None
20) (1/2, 3/2, 5/2)
22) None
24) (5/2, ½, -1/2)
26) Infinitely many
28) (-2, 3, -2)
30) (-8, 2, 2)
10.1 parabolas
February 27, 2009
Objectives
•
•
•
•
Find the equations of parabolas
Graph parabolas
Learn the reflexive property of parabolas
Translate parabolas
What is a parabola?
• A parabola is the set of
points in a plane that
are equidistant from a
fixed point and a fixed
line.
• The point is called the
focus.
• The line is called the
directrix.
Equation of a parabola with a vertex
(0, 0) with a vertical axis.
• The parabola has…
…a focus at (0, p)
…directrix y=-p
It opens upward when p>0.
And the equation…
x2=4py
Equation of a parabola with a vertex
(0, 0) with a horizontal axis.
• The parabola has…
…a focus at (p, 0)
…directrix x=-p
It opens right if p>0.
And the equation…
y2=4px
Sketching a graph
x2 =8y
Find the equation of a parabola
Focus (-1.5, 0)
Directrix, x=1.5
Translations of parabolas
Vertical axis
(x-h)2=4p(y-k)
Vertex (h, k)
Focus (h, k+p)
Directrix, y= k-p
horizontal axis
(y-k)2=4p(x-h)
Vertex (h, k)
Focus (h+p, k)
Directrix, x=h-p
Graphing
y=(x-2)2+4
Your assignments
p. 853
41-48
59-74