INSTRUCTOR: Now, in this lesson, we're going to focus on graphing quadratic functions using transformations. So let's start with the parent function y equals x squared. This graph has a shape of a U, and it opens upward. It looks like that. 

Now, what do you think is going to happen if we put a negative sign in front of it? The graph of negative x squared. It looks very similar to the first one, but it's going to reflect over the x-axis, which means it's going to face downward instead of opening upward. 

Now, what about the graph y equals x squared plus 2? What effect will the plus 2 have on the graph? Plus 2 will cause it to shift 2 units upward, so it's going to start at y equals 2, and then it's going to open upward. So that's the shape of that graph. 

Let's say if we have a negative x squared minus 1. Minus 1 is the vertical shift, so it shifts down one unit. So it's going to start at negative 1. And because there's a negative in front of the x squared, it's going to open downward, so it looks like that. 

Now, what about this one? y is equal to x minus 1 squared. This graph is going to shift one unit to the right. If you're ever unsure about this, set the inside equal to 0, and you'll see that x is equal to 1. That's going to be the location of the new origin or the vertex. 

Now, let's say if we have x plus 2 squared. This one is going to shift 2 units to the left. But let's put a negative sign in front of it. So it's going to open downward. 

Try these two examples. y equals x minus 3 squared plus 2 with a negative in front, and then x plus 2 squared minus 4. So the first one is going to shift three units to the right and up 2 units, so that's the location of the vertex. 

The vertex is 3 comma 2. And because of the negative sign, it's going to open downward. So it looks something like that. 

And for the last one, the vertex is negative 2, negative 4. The graph shifts two units to the left and down 4 units. But we have a positive in front of the x plus 2 squared, so it's going to open upward. Anytime you have a positive x squared, it opens upward. If there's a negative in front of the x squared, it's going to open downward.