Parabola Investigation Parabola song http://www.youtube.com/watch?v=IvXgFLV2gOk

y = x2 y = -x2 y = -5x2 y = 3x2

y = x2 y = 2x2 y = ½ x2 y = 1/8 x2

y = x2 y = x2+1 y = x2-2 y = x2+3

y = (x+1)2 y = x2 y = (x+3)2 y = (x-1)2

Find the coordinates of the vertex for each of the graphs (0,0) y = x2 (0,1) y = x2+1 y = x2-2 (0,3) y = x2+3 (0,-2) Find the coordinates of the vertex for each of the graphs

Find the coordinates of the vertex for each of the graphs y = (x+1)2 (0,0) y = x2 (-1,0) y = (x+3)2 (1,0) y = (x-1)2 (-3,0) Find the coordinates of the vertex for each of the graphs

2 1 y = 2x2

1 3 6 (2 lots of 3) y = - ( x + 4 )2 + 5

Graph the following functions and find the vertex of the coordinates 1. y = (x + 2)2 – 3 vertex ( , ) -2 -3 2. y = -3(x - 1)2 + 4 vertex ( , ) 1 4

Where a, h, and k are all constants According to the function y = a ( x – h )2 + k Where a, h, and k are all constants What would the vertex be? What variable would tell us if the parabola is opening up or down? How can you tell if the parabola will open “fat or skinny”? (h, k) +a up, -a down 0 < a < 1 fat, a > 1 skinny

Sketch graphs of the following functions. Locate the vertex, determine the direction of the curve, and decide on the width of the curve. y = x2 - 6 y = 3(x - 4)2 y = -1/6 (x + 4)2-3 y = -2 x2 + 5