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    • 3.1: Graphs of Quadratic Functions

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    Graphs of Quadratic Functions

    A Quadratic Function is any function defined by a polynomial whose greatest exponent is two.

    That means it can be written in the form \(f(x)=ax^2+bx+c\), with the restrictions that the parameters \(a\), \(b\), and \(c\) are real numbers and \(a\) canNOT be zero.  

    The graph of any quadratic function is a U-shaped curve called a parabola.

    There are certain key features that are important to recognize on a graph and to calculate from an equation.

    Key features of a parabola

    1. The orientation of a parabola is that it either opens up or opens down
    1. The vertex is the lowest or highest point on the graph
    1. The axis of symmetry is the vertical line that goes through the vertex, dividing the parabola into two equal parts.

      If \(h\) is the \(x\)-coordinate of the vertex, then the equation for the axis of symmetry is \(x=h\).

    1. The maximum or minimum value of a parabola is the \(y\)-coordinate of the vertex.
    1. The

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