Video Transcript
Describe the sequence of the operations of the graph ๐ฆ equals ๐ฅ squared that produces the graph of ๐ฆ equals ๐ฅ squared minus six ๐ฅ plus 14.
In order to do this, we need to get our equation in vertex form. So to do that, we need to group the first two terms together. Check to see if there is a GCF that isnโt a variable, and thereโs not.
And now we need to take ๐ over two squared, which is negative six over two squared, which is nine. And we add it to that inside of the parentheses, which means weโll also have to subtract it outside of the parenthesis so the equation stays balanced.
Now the whole point of doing this is so that way the parenthesis becomes something squared. And it becomes ๐ฅ minus three squared because negative three times negative three is positive nine and negative three plus negative three is equal to negative six and then negative nine plus 14 equals five.
So looking at our vertex form, โ moves our equation left and right and ๐ moves our equation up and down.
So notice itโs ๐ฅ minus โ and we have ๐ฅ minus three, so we must have plugged in a positive three. So it was moved right three and up five, so we will shift three to the right and then up five.