Math T2

Math T2

1. parabola

   • h translates horizontal translation
     • h translates the basic parabola "h" units along the x axis.
       • e.g. (x-2)^2 = right - shifted from the origin
       • (x+2)^2 = left - shifted from origin
   • when given a rule a = x > 1 or a = x < 1
     • x > 1 -> the narrower
     • x < 1 the wider
     • y=ax^2
       • "a" is the dilation factor. The larger "a" is, the narrower or thinner the graph is. If a is a proper fraction (a>0 but a < 1) the graph is wider than y=x^2
   • (x+ h) means negative & translates to the left
   • reflection
     • axis of symmetry
     • y = x^2 -> parabola above x axis
     • y = - x^2 -> parabola is flipped
   • Questions
     • What transformations are made for the following from the original graph of y = x^2
       • a) y = 3x^2 - 1
         • becomes narrower, translates down 1
       • b) y = 1/2x^2 + 4
         • wider, translating up by 4
     • (h,k) when y = 2(x-4)^2 +6
       • (4,6)
     • y = a(x-h)^3 + K
       • graph has 2 lines that curve
     • y = 2(x+3)^2 - 4
       • 1) formula 2) identify the value of a, a =2
         • 3) effect of a: y=x^2, dilated by 2, closer to the y axis
           • 4) value of h, h=-3 5) effect of h, 4 units to the left
             • 5) effect of h, 3 units to the left 6) value of K, K=-4
               • 7) effect of K, 4 units down
     • y = 2 (x-1)^2 + 2
       • coordinates of turning point, intercepts witht eh axes
         • 1) y=a (x-h)^2 + K
           • 2) values of variables
             • 3) statement on the basic parabola: y=x^2, y direction, factor of 1/2, wider than the basic curve, translate 1 unit to the right, 2 units up
               • 4) shape of the parabola: positive or negative. since a>0, parabola is positive
                 • 5) coordinates of turning point (h/k)
                   • 6) y intercept, x = 0
                     • 7) sketch the graph