Monday 10/14/13 Function Transformation
Post date: Oct 11, 2013 8:59:44 PM
Notes:
Using the graph of f(x)=x^2 as a guide, we're going to learn the tranformations of a graph.
If a parabola opens upward, it has a lowest point. If a parabola opens downward, it has a highest point. This lowest point is the veretx of the parabola.
In order to tranform the basic quadratic form y=x^2 into the usual formula of y=a(x-h)^2+k, you would have to carry out the following transformations:
1. a horizontal shift of h units to the right.
2. A vertical stretch by a factore of a (which will ao incorportate a reflection across the x-axis if a is negative.)
3.A vertical shift by k unites upwards.
The horizontal shift will move the vertex of the quadratic from (0,0) to (h,0) and the vertical shift will move the vertex from (h,0) to (h,k). This is why the vertex of the quadratic occurs at the point (h,k)
Example:
In this problem, h=-1 and k=7, so your vertex would be (-1.7)
a=3, which means you have a vertical stretch by 3
k=7, you will shift the graph upward 7 units
h=-1, you shift the graph to the left 1 unit.
Other resource:
HW: Quad Packet, due next Tuesday, 10/22