MODULE III As we had previously discussed, this section will be all about learning how to transform figures.
MODULE III A translation is the first we’ll discuss. A translation is when I keep the figure exactly as it is, but slide it up or down and left or right. We call this a rigid motion.
MODULE III To mathematically move a parabola we must alter the equation a bit. To move a parabola up or down I must alter the k element. To move a parabola left or right I must alter the h element.
MODULE III If this had been my original equation… 4(y – 5) = (x – 2) 2 I could move it up 2 spaces and right 4 spaces by altering the equation like this… 4(y – 5 – 2) = (x – 2 – 4) 2 4(y – 7) = (x – 6) 2
MODULE III Notice that when I move to the right my change is negative as is the case with upward movement. When I move downward and left my change is positive.
MODULE III So let’s try one… If this had been my original equation… 4(y + 3) = (x – 4) 2 Move this graph 2 units the right and 1 unit downward. 4(y + 3 + 1) = (x – 4 – 2) 2 4(y + 4) = (x – 6) 2
MODULE III When you actually graph these, you will be able to see that this is true. If you find out the movements are NOT accurate, then you know that you have done something wrong!