Quadratic Equations and Functions
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
You can always use making a table to graph anything you want to in Math class. I’m going to make a table to graph this y equals x squared take away 2. So I chose some x numbers both positive and negative ones and I’m going to substitute them in one by one, to find their corresponding y's.
Like -3 times itself is +9 take away 2 is 7. -2 times itself +4, take away 2, 2. I’ve already done this ahead of time, so I’m going to fill in a couple of blanks here. Now I’m going to stop there, because when I was making this table I stopped there when I saw my symmetry come into play. I saw that -1 showed up again, so I knew there was going to be symmetrical around that, that’s going to be my Vertex. 7 is going to show up here. That’s great.
You can use ideas like that to speed up these homework problems. They take a long time if you have to go through and do all of these different point’s one at a time. But if you can identify the symmetries kind of like it's rainbow thing, it will make your graphs be a lot more quick.
The other thing I wanted to show you is the Vertex. It’s the place that my symmetry happens around. It’s also the place that my Axis of Symmetry will show up on the graph. Let me show you the graph. Let’s move over here. My first dot is going to go at (-3,7). -3 1, 2, 3, 4 , 5 , 6 , 7, -2, 2, -1, -1, 0, -2.
This is where my symmetry started to happen. At this point in my table, I saw that I could turn back around with my y values. So instead of looking at my table anymore, I’m done. Like I know my next dot is 1,-1 it’s behind my head. I’m like reading backwards behind the eyes in the back of my head. 2, 2 is in there and then I have 3,7, I think that was. Because I’m not counting the boxes, I just know symmetrically that this point is going to be reflected across that Axis of symmetry, that goes through the Vertex. There is my parabola connected with a smooth u-shape and that’s how I can graph these parabolas without taking too much time. Look for the symmetry, both in the table and on your graph. It makes these people go a lot more quickly.