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, 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… x 2 =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… y 2 =4px

Sketching a graph x 2 =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