Video: Horizontal and Vertical Shifting of Graphs

Describe the sequence of operations on the graph of 𝑦 = 𝑥² that produces the graph of 𝑦 = 𝑥² − 6𝑥 + 14.


Video Transcript

Describe the sequence of the operations of the graph 𝑦 equals 𝑥 squared that produces the graph of 𝑦 equals 𝑥 squared minus six 𝑥 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 isn’t a variable, and there’s not.

And now we need to take 𝑏 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 we’ll 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 𝑥 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, ℎ moves our equation left and right and 𝑘 moves our equation up and down.

So notice it’s 𝑥 minus ℎ and we have 𝑥 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.

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