The Vertex and Axis of Symmetry - Problem 1
Finding the vertex from a graph is really easy. You just look for the highest or lowest point of a parabola. Finding the vertex from an equation is a little trickier. You do have to remember how to find the x coordinate. The way to find the x coordinate and that’s your first step is to find -b/2a. Once you’ve found that value, you’re going to substitute it back in to find your corresponding y value.
Here is what I mean, -b/2a in this situation is going to be -6 over 2 times 1 which is equal to -3. That tells me the first or x coordinate of my vertex is going to be -3. To find the y value, I need to plug in -3 for my x substituting and find the corresponding y. Y is going to be -3 squared plus 6 times -3 plus 8. Do that out, I’ll have 9 take away 18 plus 8, moving from left to right, that’s -9 plus 8 which is -1. Okay there we go. That’s the Vertex for my parabola. I’m done with the problem.
If I wanted to I can graph that to verify, or if I had to make a graph to begin with, I know this parabola opens up and the vertex, or the lowest point is (-3,-1). So I already in my head can kind of visualize that this parabola is going to look something like that.
So this is how a vertex can be useful if you have to graph something, you start by finding the x coordinate, you find the corresponding y value, and it helps you wrap your head around what the sketch of that parabola might look like.