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The Vertex and Axis of Symmetry - Concept
In a parabola, the vertex is the highest or lowest point on a parabola. To calculate the vertex of a parabola, we can first calculate the x-value by dividing the opposite of the " b" value by 2 times the "a" value. The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward. The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.
One of the things that you're really going to want to know about if we're graphing parabolas is how to find the vertex, and also how to find the axis of symmetry. They're pretty easy once you get the hang of it.
First thing is let's talk about definitions. The vertex is the highest or lowest point on a parabola. The x value is x=-b over 2a, the y value is found by substituting the x value. Let me draw you a picture. The vertex is the highest point of a parabola if the parabola opens downward, there's the vertex there or the lowest point if the parabola opens upward. That's how you can find the vertex from a graph or that's what it means visually. And this is how to find the coordinates algebraically.
So once you have an idea of what the vertex means, the axis of symmetry makes more sense. So me back up a little bit and talk about the axis of symmetry. The axis of symmetry is the line that cuts the parabola into two matching halves and whose equation is x=-b over 2a. Do you recognise that? The -b over 2a piece? That's the same thing as the x coordinate of the vertex. So if I go back to my picture, I can show you guys here what the axis of symmetry looks like. It's the vertical line that goes through the the vertex like that. It cuts the parabola into two matching halves, and it has the equation x=-b over 2a just like the x coordinate of the vertex. That's really useful when you're drawing graphs. This axis of symmetry business can help you get some points on geograph without having to do mathematical calculations.
So these are two important definitions, make sure you have them in your notes and more importantly make sure they make sense to you in your head.