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2.3 Quadratic Functions

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A quadratic function is a function of the form:

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Properties of the Graph of a Quadratic Function Parabola opens up if a > 0; the vertex is a minimum point. Parabola opens down if a < 0; the vertex is a maximum point.

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a > 0 Opens up Vertex is lowest point Axis of symmetry Graphs of a quadratic function f(x) = ax 2 + bx + c a < 0 Opens down Vertex is highest point Axis of symmetry

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Steps for Graphing a Quadratic Function by Hand Determine the vertex. Determine the axis of symmetry. Determine the y-intercept, f(0). Determine how many x-intercepts the graph has. If there are no x-intercepts determine another point from the y-intercept using the axis of symmetry. Graph.

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Without graphing, locate the vertex and find the axis of symmetry of the following parabola. Does it open up or down? Vertex: Since -3 < 0 the parabola opens down.

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Finding the vertex by completing the square:

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(0,0) (2,4)

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(0,0) (2, -12)

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(2, 0) (4, -12)

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(2, 13) Vertex

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Determine whether the graph opens up or down. Find its vertex, axis of symmetry, y-intercept, x- intercept. x-coordinate of vertex: Axis of symmetry: y-coordinate of vertex:

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There are two x-intercepts:

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Vertex: (-3, -13) (-5.55, 0)(-0.45, 0) (0, 5)

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