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A quadratic function is a function that can be written in the form where a , b , and c are constants and Note that in a quadratic function there is a power of two on your independent variable and that is the highest power. Standard Form of a Quadratic Function Sometimes your quadratic function is written in standard form. It is ok to leave it in this form when working with your problem. I will be showing you how to graph a parabola using either form. Graph of a Quadratic Function The graph of a quadratic function is called a parabola. It is basically a curved shape opening up or down. What does a tell us?
When you have a quadratic function in either form, OR , if a > 0, then the parabola opens up , if a < 0, then the parabola opens down . Vertex

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The vertex is the lowest or highest point (depending on direction) on the graph of a quadratic function. Finding the vertex using the form , : ic function is in the form , , then the vertex = . Basically you will find the x value of the vertex first and then just plug that value into the function to get the y or functional value of the vertex. Finding the vertex using the form : If your quadratic function is in the form , then the vertex = ( h , k ). Axis of Symmetry Each parabola is symmetric about a vertical line called the axis of symmetry. This
Think of it as a mirrored image about this vertical line. The next three graphs illustrate the different aspects of the graph of a quadratic function or parabola. The following is the graph of the function : I want you to note a few things about this graph: vertex is the lowest point on the graph. It is either going to be the lowest or highest point on the graph of a quadratic f Second, look at the axis of symmetry . It is not actually part of the graph itself, but is important in that the parabola creates a mirrored image about it. Note how it is symmetric about the axis of symmetry. Also, note how it goes through the vertex. Third, note how there is

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